The former Liverpool coach had initially agreed to join Brighton & Hove Albion, but reversed his decision once the Premier League outfit came calling.
The 55-year-old will take on the role as first team assistant coach, while Watson has been appointed as senior goalkeeping coach.
The news comes just a matter of weeks after Koeman was named as Mauricio Pochettino's successor at St Mary's.
Martin Hunter, who spent four years in charge of the development squad at Southampton, has also been appointed as technical director.
Executive director Les Reed told the club's official website: "I am extremely happy that we have been able to appoint three highly-respected and talented coaches to these important positions in our coaching structure. Sammy has a wealth of experience from his time with Liverpool and Bolton, as well as from his long association with the England team.
"Despite his relatively young age, Dave has already built up an impressive CV and is regarded as one of the most talented goalkeeping coaches in Europe, and has only just returned from the 2014 FIFA World Cup finals.
"That we have been able to attract Sammy and Dave to Southampton is testament to our ambition to continue growing as a club, and shows our commitment to develop talented footballers at all age levels."
The pair will work with Koeman, his brother Erwin and Jan Kluitenberg.