SuPer chair Juhani Palomäki says his group will sign the contract on Monday, although the two unions had previously agreed to sign it together or not at all.
Tehy says it will decide by October 9 whether it will issue a strike warning.
The offer promises a 12 percent raise over the coming two and a half years.
While the rank and file of SuPer was almost evenly split over the issue, the delegate council of the union endorsed the contract by wide margin on Thursday.
Local authorities insisted that the 12 percent offer was absolutely the last one, and Prime Minister Matti Vanhanen warned that even this offer may be too expensive for local governments. On Saturday he called Tehy's rejection "regrettable" but reiterated that the government would not offer any more money to raise municipal wages.
The approval of the contract by SuPer was expected to dampen Tehy's bid for higher wages.