Woods will play alongside Rory McIlroy and Masters champion Adam Scott in a group containing the world’s top three, with Garcia paired with former Open champions Padraig Harrington and Stewart Cink.
Garcia escaped punishment for what could be construed as a racist remark about Woods after offering an unreserved apology for his “stupid and out of place” comments at the European Tour’s annual awards ceremony ahead of the BMW PGA Championship last month.
During a Q&A session involving the full Ryder Cup team, the 33-year-old was asked if he would invite Woods to dinner one night at Merion next month to settle their differences, which resurfaced at the Players Championship at Sawgrass.
“We will have him round every night,” Garcia said. “We will serve fried chicken.”
After finishing 19th at Wentworth, Garcia said he had been asked to wait until Merion to apologise in person to Woods, who said last week: “It’s already done with. It’s time to move on.”
Garcia’s group will tee off at 7:44am local time from the 11th hole in the first round, with Woods, McIlroy and Scott starting at 1:14pm from the first.
Ryder Cup team-mates Luke Donald, Lee Westwood and Martin Kaymer start at 12:52pm from the first with 2010 champion Graeme McDowell in the following group with 2003 winner Jim Furyk and former Masters champion Zach Johnson.
American Webb Simpson gets the defence of his title under way at 1:36pm alongside Open champion Ernie Els and 2012 US Amateur champion Steven Fox, while Belgium’s Nicolas Colsaerts is in the second group out from the 11th at 7am, just ahead of four-time major winner Phil Mickelson.
The full field will only be completed on Sunday evening after the conclusion of the Lyoness Open on the European Tour and FedEx St Jude Classic on the PGA Tour, with the world’s top 60 securing their places in the year’s second major championship.
There are four Scots in the field next week. Martin Laird will play his opening two rounds with South African George Coetzee and German Marcel Siem; Chris Doak has been grouped with American pair Andrew Svoboda and Doug Labelle II; Paul Lawrie tees off with Australian Geoff Ogilvy and Angel Cabrera of Argentina; and Russell Knox plays with American amateur Max Homa and his compatriot Matt Bettencourt.