The 26-year-old has agreed terms to sign a 12-month contract with an option to extend it beyond the end of next season, with the player having already passed a medical at The Vetch.
Trundle will be reunited with Swans director of football Brian Flynn - the manager who gave the hit-man his first opportunity in league football with The Dragons, when he signed him from Welsh side Rhyl in February 2001.
He was a key player in Wrexham's promotion to Division Two last term but at the end of last season, the player opted against signing a new deal at the Racecourse Ground for a move elsewhere.
Trundle joins former Dragons team-mate Andy Morrell in leaving Denis Smith's side this summer, with the Wrexham manager having replaced the duo with the signings of Chris Llewellyn and Chris Armstrong.
Flynn was delighted to sign Trundle and is pleased with the way his squad is shaping up for the new season.
"He's a big signing for us," Flynn told planetfootball.com.
"I signed him first over two years ago and I'm delighted to get him again.
"I'm happy with the quality (of squad) that we've (now) got."
Flynn is also hoping of bring in more fresh faces, as he looks to improve the fortunes of the club in the following campaign.
"We've signed 15 and we could do with a couple more," added Flynn to BBC Wales.
"We're particularly looking at the centre of defence, but I'm very happy with the way the squad is coming together."
