A negotiator, Ayad Sammarai from the Iraqi Islamic Party announced his group's support for the charter, following talks with Shi'ite and Kurdish leaders Tuesday.
The groups reached a breakthrough in a deal to allow parliament next year to consider amendments to the constitution.
For months, Sunnis have opposed the constitution over fears that the proposed federal system would break up the country and weaken Sunni influence.
It is unclear if other Sunni groups not involved in Tuesday's talks will reverse their calls for voters to reject the constitution.
U.S. officials have also been pressing Sunnis to back the constitution in the hope it will weaken the insurgency and enable the withdrawal of foreign troops.
Meanwhile, at least 40 people died in a series of attacks, which officials have warned may increase ahead of Saturday's vote.