(Updates with governor signing bill)

May 27 (Reuters) - Michigan lawmakers on Tuesday voted to raise the minimum wage to $9.25 per hour by 2018, joining other U.S. states and municipalities that have considered increases in the minimum wage this year.

The increase in the minimum wage was approved by bipartisan votes in both chambers of the Republican-controlled Legislature. The House vote was 76 to 34, while the Senate vote was 24 to 12.

Republican Governor Rick Snyder signed the bill into law later on Tuesday.

"This is something that is good for Michigan," Snyder told a news conference. "It's good for the hard-working people of Michigan and I believe economically sound."

The law ties the state's minimum wage to the rate of inflation starting in 2019, capped at 3.5 percent per year, and sets the minimum wage for workers earning tips such as waiters at 38 percent of the minimum wage for non-tipped workers.

Michigan's current minimum wage is $7.40 per hour for non-tipped workers and $2.65 per hour for tipped workers.

Minimum-wage increases have been considered in 38 states this year in a national push by Democrats. Minnesota was among the states to approve an increase in the minimum wage to $9.50 per hour for large businesses by August 2016.

President Barack Obama urged Congress to raise the federal minimum wage to $10.10 per hour from $7.25, but did not win the backing of the Republican-led U.S. House of Representatives.

In Michigan, the approval of the minimum-wage hike came a day before a deadline for a group to turn in signatures to put a ballot proposal before voters to raise the minimum wage to $10.10 per hour by 2017 and index wage increases to inflation.

Senate Majority Leader Randy Richardville said he had concerns about the ballot proposal.

"Restaurants, tourism, young people would have suffered," he said. "I don't think it was the intent of those who drew up the ballot proposal, but it had some serious problems in it."

By tying the increase in the minimum wage to an index, the debate can be taken off the table for a long time, he added.

"Michigan families are working harder than ever, and they deserve a raise," said Representative Tim Greimel, the House Democratic leader.

(Reporting by David Bailey in Minneapolis and Karen Pierog and Mary Wisniewski in Chicago; Editing by Jan Paschal and Eric Walsh)