Allardyce has been out of the game since being sacked by England in late September.
"We are delighted to be able to make an appointment so quickly and fortunate that someone of Sam's calibre and experience was available," Eagles chairman Steve Parish said, a day after sacking Alan Pardew.
Allardyce's first game in charge will be Monday's English Premier League match at Watford.
Allardyce was seen at the south London club's training ground for talks earlier Friday.
Speaking to Sky Sports News television, Allardyce, 62, described Palace as a "fantastic" opportunity to return to Premier League management.
Pardew was sacked on Thursday following a miserable run of results, with the Eagles winning just four of their 17 league matches this season and only one of their last 11.
Palace are only one point above the relegation zone.
Allardyce has been out of the game since being sacked by England in late September after just one match in charge following ill-advised remarks to undercover reporters.