Remy, 29, reunites with Alan Pardew who he played under at Newcastle United during the 2013-14 season. The France international sat third in the pecking order at Stamford Bridge behind Diego Costa and Michy Batshuayi and is eager to rediscover the form that saw him score 14 goals in 26 appearances during his time on Tyneside.
"Loic has been a target of mine throughout this transfer window and I'm delighted the deal has been done," Palace boss Alan Pardew said. "I brought him to Newcastle so I know what he is capable of and I am convinced he will be a quality addition to our squad as we evolve.
"Loic has international and Champions League experience as well as being a Premier League title winner and is the latest example of the high calibre of players we have brought into the club during this transfer window."
22-year-old Bamford meanwhile becomes Sean Dyche's fifth signing of the summer and the latest in an ever-growing list of youngsters to leave Stamford Bridge on a temporary deal.
Bamford had an unsuccessful stint at Crystal Palace during the first half of the 2015-16 season where he failed to start a single league game for Alan Pardew's side. The striker briefly returned to Chelsea before joining Norwich City on another loan deal, but was limited to just seven appearances.
Burnley however will be hoping Bamford can recapture his excellent form of the 2014-15 season, where he was named the Championship Player of the Year while on loan at Middlesbrough where he scored 17 times in 38 league games.
Remy and Bamford becomes the 25th and 26th players to leave Stamford Bridge this summer with Brazilian duo Kenedy and Lucas Piazon and United States youngster Matt Miazga also expected to leave in the coming days. Ghana winger Christian Atsu however looks to be the next out the door with Sky Sports reporting the 24-year-old is on the brink of signing for Newcastle United on a season-long loan deal.
Atsu, who had spells at Bournemouth and Malaga last season, is another who is yet to make a first-team appearance for Chelsea, will reportedly undergo a medical with the Championship side today (Tuesday 30 August), with Newcastle hoping to include the option to make the move permanent next summer.