The 31-year-old was not offered a new deal by Sunderland and, with his contract expiring on Sunday night, he linked up with the Hammers in a bid to maintain his fitness.
Bramble made 51 appearances for the Wearsiders after being signed for £1m from Wigan by then manager Steve Bruce during the summer of 2010.
He has also been linked with a move to Turkish club Besiktas.
West Ham travel to Ireland on Tuesday for an intensive training camp but it remains to be seen if Bramble will make that trip.
Their other high-profile signings were also at Chadwell Heath on Monday morning, although Andy Carroll did not join keeper Adrian and left-back Razvan Rat as he is still on a rehabilitation programme after injuring his heel towards the end of last season.