Norway striker Carew and former France winger Faubert are joined by Senegal pair Abdoulaye Faye and Papa Bouba Diop, all of whom were out of contract.
Right wingback Faubert made the last of his 121 appearances for the club in Saturday's play-off final win over Blackpool at Wembley.
The 28-year-old was signed from Bordeaux in 2007 under Alan Curbishley and, despite rarely living up to his £6 million transfer fee, he secured a spell on loan with Real Madrid in 2009.
Former Valencia and Aston Villa striker Carew scored twice in 21 appearances this season after joining from Aston Villa at the start of the campaign.
Defender Faye, 29, and midfielder Diop also arrived on one-year contracts last summer.
As he prepares for life back in the Premier League next season, boss Sam Allardyce has also released striker Frank Nouble, 20, and young midfielder Olly Lee, the son of former Hammers and England star Rob Lee.