The midfielder has inked a new four-year contract.
"I am delighted that the club has been able to extend Morgan's contract," Pochettino said.
"During my short time with Southampton, Morgan has shown what a capable player he is and has demonstrated his potential to become one of the Premier League's most complete midfielders.
"His work-rate and determination make him an integral part of how we play, and so I am pleased he has been rewarded with a new long-term deal.
"Morgan has played a major part in the journey this club has been on over the past four years, and I am sure he will continue to develop as a player as we move towards our long-term ambitions."