Bertrand had initially joined on a season-long loan in July but the 25-year-old signed a four-and-a-half-year deal on Monday after some impressive displays in Southampton's miserly defence, the best in the league, which has helped them to fourth place.
The permanent deal brings to an end a frustrating spell with league leaders Chelsea, where he had gone on loan seven times and rarely had a first-team look in.
Southampton also moved to improve their forward options by bringing in 23-year-old attacking midfielder Djuricic on loan.
The Serb arrives at the south coast club for the last 15 games of the season as they try to hold onto fourth spot and qualify for the Champions League.
Saints manager Ronald Koeman said he had been tracking Djuricic since his days at Dutch club Heerenveen.
"I know the player from Holland," Koeman told Southampton's YouTube channel. "He played several seasons for Heerenveen and then he moved to Benfica.
"He had some good games, there was a lot of interest in the player when he was at Heerenveen. He moved to Portugal and now it's a good chance for the player to develop himself."
Koeman will hope Djuricic has a similar impact to Eljero Elia, who was signed on loan from Werder Bremen last month and has already made his mark at Southampton.
"It's difficult for young players to make the step to teams like Benfica, it's physical football in Portugal and the player is more technical," Koeman said.
"I think it's better for him to play in a team like Southampton because our type of football is the best for Djuricic."
(Reporting by Martyn Herman, editing by Tony Jimenez/Peter Rutherford)
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