The experienced centre-back grew up watching the club and says he has fulfilled an ambition by signing for them.
Swaine, who last season played for Maidstone United, knows Mark Goldberg well.
He was the new manager’s captain for four years at Bromley - and together they took the club up from the National League South.
That’s the goal again and the defender, 31, says it’s a great move for him.
Swaine told the club’s website: “Welling is a club I’ve known about for a long time and they were unfortunate not to get promoted last season.
“I’ve worked and been successful with Mark (Goldberg) and Hugo (Langton, coach) before so I’m very happy to be on board.
“Last season was a bit of a disappointment for me, despite playing well personally.
“I’m sure that he and the coaching team can attract the right players and build a successful side. It will be a tough league again but I’m really looking forward to getting going.”