The 26-year-old spent five years at Wolfsburg, making more than 150 appearances for the Bundesliga club. He also has three international caps for Iran.
"I'm very happy to come and play in the Premier League," Dejagah said.
"I know Sascha Riether, (Fulham's German right back] well and he told me very good things about the club."
Dejagah has signed a three-year deal with the Londoners.
Berbatov, the 31-year-old striker has moved for an undisclosed fee and will be reunited with Martin Jol, who managed Tottenham during the Bulgarian's time at the north London club.
Berbatov, who scored 56 goals and made 149 appearances for Manchester United, said: "I'm delighted to have signed for Fulham and I look forward to playing under Martin Jol once again.
"As soon as I was aware of Fulham's interest my decision to join was an easy one to make.
"I'm impressed with the set-up here and the people have made me feel welcome. There is a close and personal feel around the club and I can't wait to get started."
Kieran Richardson has also completed his move from Sunderland to Fulham.
The 27-year-old, who was born in London, signed a three-year deal, with an additional year's option, for a undisclosed fee.
He said: "I'm delighted that my transfer to Fulham has been completed and now I'm eager to start training for my new club straight away and pulling on the white shirt for the first time."
Richardson made 149 appearances for the Black Cats after signing from Manchester United in 2007 shortly after lifting the Premier League trophy.
Jol said: "Kieran is a proven top-level player, who has the versatility to play a number of positions.
"He will bring all-round quality which will add strength to our squad and I'm confident that he will adapt well to our style of football, and make an impact for us."
Sunderland manager Martin O'Neill replaced Richardson by securing Tottenham defender Danny Rose on a season-long loan.