Byrne, 30, was released by the Iron this summer after nine seasons at Glanford Park.
He made two trial appearances for Preston North End, but also trained with the Latics - signing a deal on Thursday.
"Cliff had been on our radar all summer and there was a lot of competition to sign him," Dickov told Oldham's official website.
"Yet again, however, he was a player who wanted to come to us. He likes the training and atmosphere at the club. Cliff has played a lot of games and above all is a leader, both on and off the pitch.
"I have seen a lot of Cliff and he is comfortable at both centre-back and right-back.
"I am delighted the way our recruitment has gone and we needed experience, which Cliff provides, not just at the back but throughout the whole team."
Iron fans will get the chance to see Byrne in claret and blue one final time on Sunday, when more than 40 former players return to North Lincolnshire for his benefit match.
The 2009 League One play-off winning side will come back together to take on a team consisting of other Iron players from Byrne's spell at the club.
That means a return for Nigel Adkins, manager in 2009 and now in the Premier League with Southampton, for the first time along with the now Celtic striker Gary Hooper.
It will also see Billy Sharp and Andy Keogh reform their potent strike partnership, in the select side that also includes Peter Beagrie, Martin Paterson and Alex Calvo-Garcia.