The influential British artist, who once turned down the chance to paint the monarch because he was too busy, said: "I have planned a landscape full of blossom that's a celebration every year."
The tall 20ft x 6ft window - one of the church's few remaining clear ones - will be known as The Queen's Window and is in the north transept of the gothic Abbey.
The cost is being covered by two anonymous benefactors.
Westminster Abbey said Hockney would largely have artistic control - but be given guidance from the Dean and Chapter and the Westminster Abbey Fabric Commission who deal with changes to the historic building.
"He's given a very elliptical hint. We're as interested as everyone else to see what he comes up with. He will have pretty much free rein because he's David Hockney," an Abbey spokesman said.
"The Queen is certainly aware of the proposal and there will be continual briefings from us."
The Dean of Westminster, the Very Rev Dr John Hall, came up with the idea of approaching Hockney to help celebrate the Queen's reign.
Bradford-born Hockney, widely considered to be the country's greatest living artist, burst on to the scene in the early 1960s as one of the leaders of British pop art.
