The Chelsea forward joined the Welsh club on a season-long loan deal earlier this week.
Abraham scored 26 goals in the Championship for Bristol City last season, and Mawson believes he can repeat his exploits in England's top flight.
"I am confident he will prove himself in the Premier League. He has a lot of potential, and I think he can fulfil that during his time here," Mawson told the club's website.
"He gives us something different to what we have got. While Fernando is a strong striker who holds the ball up and is an aerial threat, Tammy's movement is fantastic – he makes runs and pops up at the very worst time for a defender.
"He is only 19, and for him to have scored so many goals in the Championship last season shows what quality he has already.
"He has got the tools to succeed and go far in the game."