Bridge is now a free agent after successfully terminating his contract with Thai club Chiangrai United last week due to ongoing contractual issues.
Two of Bridge's former clubs Newcastle Jets and the Western Sydney had expressed interest in re-signing the 31-year-old.
But it is understood the Wanderers, who have maintained contact with Bridge since he left the club last May after their grand-final loss to Adelaide, have won the race for his signature.
Bridge will join a strikeforce at the Wanderers that includes Lachlan Scott, Jasjua Sotirio, Brendan Santalab, Abraham Majok and new Spanish signing Oriol Riera.
The striker enlisted the help of the players union, Professional Footballers Association (PFA) and used FIFA rules to affect his release from Thailand, after months of problems at the club.
“The PFA has provided support to Mark over the past six months,” PFA Chief Executive John Didulica said in a statement last week.
“As a result of circumstances at the club, Mark terminated his contract for just cause in accordance with FIFA regulations. As a consequence, he is now a free agent and entitled to sign with a club of his choosing.”
Bridge scored seven goals in 14 appearances for Chiangrai United, after joining the Thai Premier League side in May last year.
Wanderers fans will no doubt be happy to welcome Bridge back to the club, after four very successful years with Western Sydney in which he scored 28 goals in 95 appearances.
He was part of the Wanderers side that won a premiership in the club’s inaugural season in 2012-2013, he also helped the side reach two A-League grand finals and win the Asian Champions League three years ago.
Bridge also had memorable stints at Sydney FC and Newcastle, scoring the winner for the Jets in the 2008 grand final.
Bridge won the double with the Sky Blues and scored a goal in the 2010 grand final, which Sydney FC went on to win on penalties against Melbourne Victory.
In total Bridge has bagged 58 goals in 225 A-League appearances.