Last week’s elections left them with 30 of the 60 seats — Labour has 23, the Conservatives seven.
There will be a Labour mayor, Councillor Shoab Akhtar, who will have a casting vote if decisions are tied.
However, the Tories could also decide to back the Liberal Democrats.
All the changes will take effect from the annual council meeting on May 21.
Conservative leader Philip Rogers said before the election results that he would support the largest party if there was no overall control of the council — “provided there is support for Conservative policies.”
Liberal Democrats, who made four gains at the polls, met on Saturday and decided to form an administration to run the council.
Councillors Howard Sykes and Jackie Stanton were also re-elected unanimously and unopposed as leader and deputy leader of the group.
And they plan all-party talks this week to offer some roles to opposition councillors.
Councillor Sykes said: “People clearly voted for a change, and, as the largest party, it is our duty to form an administration.
“However, we recognise we do not have an overall majority and will be seeking to work constructively with the other two parties.
“We intend to propose a Lib-Dem cabinet, and it will be for the other parties to decide if they wish to deny the will of the people from Thursday’s election.
“However, we will ensure the other parties are offered a fair proportion of both seats and leading positions.”
Oldham’s two Labour MPs have been mourning the loss of “great” Labour councillors.
Oldham West and Royton MP Michael Meacher said: “This is by far the worst local election results I can remember. We have been deprived of some of the best councillors nationally.
“The one silver lining is that this set-back is so severe it will force the fundamental change of direction of policy that is needed for party renewal.”
Oldham East and Saddleworth MP Phil Woolas agreed, saying: “David Jones’s (the former Labour council leader) administration was a great one. Clearly the Labour Party has to pick itself up by the bootstraps as we have done before.”
