The centre-backs have plenty of experience between them with Gayle having played for the likes of Dagenham & Redbridge, Whitehawk, St Albans City, Bishop's Stortford, and Welling United, he ended last season at Wealdstone.
Wassmer is someone who was managed by Hampton & Richmond Borough last season.
While Wheeler is a winger who has previously played for Charlton and Dag & Red.
"I've known Gayle for a long time, he came to me a few years ago when he was a young kid at Dagenham.” Dowson told the club’s website.
“I think we need his pace & his power in the squad. There was a couple of clubs that came in for him so we're delighted to get him.
Speaking of Wassmer, Dowson said he was pleased to get him in.
"He was named in the National League South Team of the Season and was my best player last season at Hampton, so I'm delighted to get him on board.
"He'll be our best player this season he will, he's a leader and is everything you want from a centre-half. He'll head it, kick it, and do all the defensive duties well."
Dowson revealed he has wanted Wheeler for a while.
"I remember him playing for Tonbridge and watched him in a game against Staines and thought that's the sort of lad I want.
"I've followed his career, the last move didn't work out quite well for him but it'll certainly work out here. He's an exciting winger, let's get him one-on-one with fullbacks."