The performance will be overseen by Chic's Nile Rodgers, who produced Bowie's hit album Let's Dance in 1983.
"The tribute will be a multisensory testament to the icon's incredible artistry and a reflection of his limitless creativity," said the Recording Academy in a statement.
Gaga has previously credited Bowie as an inspiration.
"He's sort of like an alien prince," she once told chat show host Alan Carr. "Every morning I wake up and I think, 'What would Bowie do?'"
"We had already booked Lady Gaga on this year's show, but when David passed - almost in a single moment - we knew we had to change direction," said Ken Ehrlich, executive producer of the Grammys.
"We immediately spoke and agreed that she should be the one to honour David. She's perfect for it."
The Grammys will be held in Los Angeles on 15 February. Gaga is nominated for best song written for visual media, thanks to her Diane Warren-penned ballad Til It Happens To You, from the documentary The Hunting Ground.
Other performers on the night include Adele, Kendrick Lamar, James Bay, Ellie Goulding and Carrie Underwood.
During his career, Bowie was nominated for 11 Grammys but only won once - when Jazzin' for Blue Jean was awarded best video in 1985. He also received a lifetime achievement prize in 2006.
The star died of cancer on 10 January, just days after releasing his new album, Blackstar. It will be eligible for honours at next year's Grammy ceremony.
A Bowie tribute is also planned for the Brit Awards, which take place on 24 February. Details have yet to be announced, but media reports suggest that Noel Gallagher, Bono, Adele and Damon Albarn have been invited to take part.

The Regatta Quay development, which includes a 20-storey building known locally as the 'wine rack', was taken over by administrators in 2010.
The Irish government owns the site after buying Irish bank debts.
The administrators said completing the ??100m buildings was dependent on the property market.
Work on Regatta Quay started in 2007, but it stopped as City Living Developments (Ipswich) Ltd, which had borrowed from the Anglo Irish and Allied Irish banks, went into administration.
Ben Gummer, Conservative MP for Ipswich, said it was "almost a metaphor" for the British economy.
"It's property speculation gone mad and a banking system which is bust, so it's going to take a lot of time to put that right," he said.
"The administrators are actively trying to find a developer to take on the work, so things are moving now but I'd like to see them move quicker."
Baker Tilly were appointed administrators for Regatta Quay by Ireland's National Asset Management Agency.
The accountancy firm is also the administrator for The Mill development next to Regatta Quay.
Regatta Quay has 118 flats built, with space for 150 more in the 'wine rack'. The Mill has 194 completed and 140 uncompleted flats.
Nigel Millar, from Baker Tilly, said: "It's very difficult to say when building work could resume.
"We'll certainly be in administration for two years. How long we'll be in administration depends on how sales progress."
Savills, which is the estate agent for the sites, said sale prices for a two-bedroom apartment had dropped from about ??300,000 in 2008 to ??175,000.
Andy Redman, from Savills, said: "If we can continue to sell at the rates we're achieving of 3-4 flats a month, then it may bring things forward, but it's dictated by market conditions."
Pop star Lady Gaga is to honour David Bowie with "an experiential tribute" at this month's Grammy Awards.
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Administrators say work will not resume on an unfinished block of flats on Ipswich waterfront until 96 completed apartments are sold.