Swansea completed three new signings on Wednesday, and another player could be joining before the end of the week.
Forbes cored 14 goals for Luton Town last season
Garry Monk, Adrian Forbes and Sam Ricketts have been formally unveiled at the club after passing their medicals.
"I genuinely believe Swansea will be in Division Two after next season," said striker Forbes, who turned down a new contract at Second Division Luton Town.
Manager Kenny Jackett also revealed he is close to agreeing a deal for Bristol Rovers defender Kevin Austin.
The 31-year-old can play at left-back or centre-back, and could form a new partnership with new arrival Monk.
"I like to play football on the floor and so I had no qualms about coming here," said Monk, who was released by Barnsley at the end of last season.
"I've not had a settled season yet in my career. I'm 25 now and need to be playing regular football. That's the only way you can improve."
Ricketts, another defender, joins from cash-strapped Conference side Telford United.