The Development Squad duo were among five players to be offered new terms when their existing terms expired over the summer.
Having joined the first team for pre-season training at new-look Staplewood earlier this week, they now join Omar Rowe and Sam McQueen in extending their contracts ahead of the 2014/15 campaign.
Goalkeeper Cropper said: “It feels great to sign.
“I think it’s a great opportunity for me as a player to come in and work hard under the new staff and hopefully earn another contract.
“The environment you’re put in [here] is one of a kind. Everybody has been saying that the new building here is five-star and it only looks to be getting better.”
Sinclair echoed his teammate’s thoughts, saying: “I’m delighted to sign.
“I’ve been here since I was eight and hopefully I can carry on progressing as I was last season and hopefully I can get in the manager’s plans for this season.
“It’s good to be here and hopefully, when I get started, I’ll kick on here and sign another new deal.”
Cropper, 21, joined Southampton two years ago after leaving Ipswich Town, and has been the regular goalkeeper for the Under-21s over the past few seasons.
He trained regularly with the first team during the 2013/14 campaign, and made the substitutes’ bench a number of times as well as regularly travelling with the squad to away games.
Sinclair made his first-team debut last August, coming off the bench in Saints’ 5-1 Capital One Cup win over Barnsley.
The 20 year-old has been with the club since he was eight, and is part of the same youth intake as current teammates James Ward-Prowse, Harrison Reed, Calum Chambers and Sam McQueen.