"I believe it is a matter of conscience, fairness and preventing discrimination," Lynch told The Associated Press.
New Hampshire would become the fourth state to adopt civil unions, following Connecticut, Vermont and New Jersey. Massachusetts has established gay marriage.
Lynch had previously declined to take a public position on civil unions, though has supported expanding health benefits to same-sex partners of state workers. He came under fire from both sides for not weighing in, especially after a delay last week of the Senate vote on the House-passed bill.
The Senate votes next week, and Lynch said he is confident the legislation will pass. It would authorize civil unions beginning next year.
Fergus Cullen, the state Republican Party chairman, wasn't happy with the Democratic governor's decision.
"The Democrats are going too far, too fast, and Gov. Lynch is going along with them," Cullen said. "These are not the actions of a moderate governor.
Democratic state Rep. Bette Lasky disagreed.
"It's never going too far when you give people their rights," she said, "and I honestly believe that the majority of people in this state want to do just that and do not want to discriminate."