Liam Buckley's side, who finished third in 2012, have brought in players from their Dublin rivals and also announced new deals for nine squad members
The duo, signed from Shamrock Rovers and Shelbourne respectively, will play alongside PFAI Young Player of the Year Chris Forrester after the highly-regarded midfielder committed himself to the club for the 2013 season despite speculation about a move to England.
Jake Carroll, Ian Bermingham, John Russell, Ger O'Brien, Conor Kenna, Kenny Browne, Anthony Flood and Christy Fagan have also extended their deals at Richmond Park and manager Liam Buckley expects to announce more new signings in the coming weeks.
"We were delighted that so many players from last year were eager to sign for us again," Buckley told the club’s official website.
"It’s a sign that they are confident that we can be even more successful next year," he added.
Brennan, 28, spent just one season in Tallaght after ending a successful four-year spell with Bohemians in January 2012.
Meanwhile, Byrne links up with Pat's after previously playing under manager Liam Buckley at Sporting Fingal.
The midfielder was a regular in Shelbourne's engine room last campaign and will add plenty of experience to Buckley's side.