A week later over the phone from Los Angeles he was still not over the euphoria, but was perfectly frank about how much he had hoped for the outcome. 'I really looked at this as a campaign not just for me but for jazz in general, and for music developed by people who are really striving to raise the bar, to make the best music that they can. The determination to win, for musicians that represent that, was so strong that day after day I felt stronger and stronger, and it got to the point where I only really visualised myself receiving the award, as though there was nobody else that were nominated. It was that solid. I'm a Buddhist, and I was chanting three hours a day for that, but still when Quincy said 'and the winner is River: The Joni Letters', I was totally stunned. All that determination and everything went out the window. I was just shocked,' he recalls.

With hindsight, given the other nominees in the category, the outcome doesn't look quite so strange. The slightly staid National Academy of Recording Arts and Sciences may well have felt that Amy Winehouse and Kanye West were simply too likely to be troublesome to warrant the top honour, while neither the Foo Fighters nor Vince Gill can lay claim to Hancock's considerable gravitas. The award was also an opportunity to honour the other musicians involved in the project, a distinguished cast list of both jazz and pop performers including Wayne Shorter, Norah Jones, Tina Turner, Leonard Cohen and Mitchell, who Hancock called as soon as he could with the news.

'They rushed me out of the seat right after the show and took me to some rooms where they had TV crews waiting for the award winners, and particularly for that category, album of the year, because that's considered to be the major one. But right after that I called Joni and she was very happy for me, but I don't think she looks too kindly at the Grammys. It's not a major concern of hers,' he says.

Hancock came to prominence in the 1960s as a jazz musician with a series of fine albums for the Blue Note label, beginning with 1962's Takin' Off and including the classics Maiden Voyage and Empyrean Isles.

Concurrently with his Blue Note recording career he cut landmark albums for Columbia with one of the most influential small groups in jazz history, Miles Davis' second great quintet comprising Davis on trumpet, Hancock, saxophonist Shorter, bassist Ron Carter and drummer Tony Williams. He also took part in Davis' early 'jazz-rock' sessions where he got to grips for the first time with electric instrumentation and began to broaden his scope.

Hancock had a taste of pop success when Mongo Santamaria had a hit with his tune Watermelon Man, and after leaving Davis made forays into pop as well as undertaking more serious work, and scored a huge crossover hit with his 1973 album Head Hunters which set new sales records for jazz.

Joni Mitchell, who had made her mark as an acoustic singer-songwriter with such folkie standards as From Both Sides Now and Chelsea Morning, had also moved into rock territory in the early 70s, but by 1974 had begun to include elements of jazz in her music. Hancock listened and was impressed, and when Mitchell asked him to be involved in her 1979 sessions for an album of Charles Mingus compositions for which, at the bassist's request, she had written lyrics, he was happy to oblige.

'I was of course aware of her before that because she'd been a huge star for some time, but the first time I met her was when we started to work on the Mingus album,' he recalls.

The two kept in touch and have occasionally collaborated since, but Hancock says River was still a project that came about spontaneously.

'It wasn't something I had as a long-time agenda. It came up when I was discussing what I might do for my next record for Verve Records. The only thing I had decided about the approach was to do a record on which the music would sound beautiful. Something with the capacity to reach the heart, that was my goal, and it was someone from the record label who asked me - since I had been a long time friend of Joni Mitchell's and had many times expressed my admiration for her genius and her artistry and for her as a human being - whether I might consider doing the music of Joni Mitchell. As soon as I heard that I thought it was a wonderful idea,' he says. It was, he says, the first time he had approached songs focusing primarily on the meaning of the lyrics rather than on their melody and harmony. Some reinterpretations stayed close to the original recordings. Others were more radical departures.

Critical response to the album was positive and the jazz world has welcomed the best album Grammy, but there has been a good deal of talk of the 'right artist, wrong year syndrome'. With Mitchell's songs providing an additional thread of continuity, the album follows a popular formula of an established, credible artist performing duets with both peers and younger bankable performers still enjoying their first run of hits. Hancock's Possibilities album in 2005 was a more overtly commercial exercise in the same vein, which got two Grammy nominations but no statuettes.

Jazz fans who consider Hancock's most important recordings to have been made in the 60s and 70s might be surprised to learn that he didn't win his first Grammy until 1983 when he won for best R&B instrumental performance with Rockit.

The best album Grammy for River, however, has given his album sales their biggest boost for many years.

'It's interesting. Before the awards my sales were the lowest there had ever been for a record nominated for album of the year. One week after the Grammys in Billboard Magazine my record went from No159 to No5 - not on the jazz charts, but on the regular album charts. So far as I know that's the highest I've ever got. Head Hunters was No10,' he chuckles.

After nearly half a century in the business, however, there is no risk of the adulation going to his head. Hancock plans to maintain his busy touring schedule with various musicians. Apart from collecting his awards, one aspect of the Grammy show he particularly enjoyed was performing Gershwin's Rhapsody in Blue, with young Chinese pianist Lang Lang. 'It was such a pure joy to work with Lang Lang,' he says. 'He's so talented and so playful and full of joy and life and vitality. Very relaxed and very warm and human. I really look forward to the possibility of doing something again with him in the future, but that is going to require a lot of practice from me.'

Surprisingly, given the boost to his CD sales, Hancock is in no particular hurry to go back into the studio, and says he doesn't feel any pressure to top the success of River.

'I don't really make albums for awards,' he says. 'If I get awards that's wonderful, but that's not the focus of my records. It's to figure out something that I feel strongly about presenting to an audience and something that I feel I have a purpose in presenting, and to try to do the best job I can. It's wonderful if it sells. If it is a jazz record - and obviously the vast majority of my records are intended to be jazz records - and it does add a dimension, I'm happy not just for myself but because it illuminates jazz in general, which really needs that kind of illumination in America, where it is often overlooked.'

River: The Joni Letters is out now