Baird, 25, has joined Fulham in a £3.025m deal and has penned a four-year contract with The Cottagers.
"I am well aware of Chris's attributes as a player from my time with Northern Ireland and his qualities and versatility will be a major asset for the club next season," manager Lawrie Sanchez has said.
"Winning the Southampton player of the season award last year is testament to his continued progress and development, which I have seen first hand at international level.
"Chris becomes my second defensive signing following the arrival of Aaron Hughes and both players provide some much needed strength to our defence."