Fernando Torres will join Milan permanently on January 5 ahead of his expected return to Atletico Madrid.
Liverpool boss Brendan Rodgers has insisted Mario Balotelli will not be going out on loan in the January transfer window.
The Austria international, who played for Middlesbrough between 2005 and 2010, has joined the Hammers from Wolfsburg.
"I feel very good to be here and I am very excited about playing for West Ham," he told whufc.com.
"I am looking forward to the opportunity to play for the club and help it get good results. I will be doing my best to play well and hope I can play a part in the club achieving the targets for this season."Pogatetz left Boro for German side Hannover before moving to Wolfsburg last summer, but has made just eight league starts for the Bundesliga outfit.
He added: "First of all when I heard that West Ham wanted me, I thought it was a club I wanted to play for because they are a very traditional club, with passionate supporters.
"Secondly, it was good for to have the opportunity to come back and play in England. This is the football I want to play and I have missed playing here, I want to show what I am still capable of after five years playing in Middlesbrough."
The 30-year-old, who was signed for Boro by Steve McClaren, earned a reputation on Teesside as a tough, uncompromising defender.
Pogatetz made 158 appearances during his time at the Riverside Stadium, helping Middlesbrough to reach the UEFA Cup final in his first season only to miss the 4-0 defeat by Sevilla through injury.
He has won 52 caps for Austria.