Tim Sheehy, a wealthy Republican businessman and political novice, has defeated Senator Jon Tester of Montana, according to The Associated Press, giving the G.O.P. another seat in its new Senate majority.

Mr. Sheehy, a 38-year-old former Navy SEAL, beat Mr. Tester, the three-term Democratic incumbent, despite being dogged by controversies during the campaign. He faced scrutiny over his conflicting stories about how he received a bullet wound in his right forearm and questions about the stability of his aerial firefighting business.

But the shifting demographics of Montana, which has experienced an influx of residents, many conservative, helped propel Mr. Sheehy to victory with a strong boost from Donald J. Trump’s overwhelming advantage against Vice President Kamala Harris in the state.

With Democrats conceding West Virginia’s Senate seat to Republicans months ago, Montana figured prominently in the G.O.P.’s plans to knock Democrats out of their one-seat majority.

Mr. Sheehy was recruited to run by Republicans who believed his résumé as a combat veteran, pilot and rancher opened a path to defeat Mr. Tester, 68, a third-generation Montanan who emphasized his agricultural roots as a working farmer. First elected in 2006 after beating a Republican incumbent, Mr. Tester had held off two other G.O.P. challengers since then.

Mr. Sheehy’s campaign was rocky. His account of suffering a gunshot wound in Afghanistan was sharply challenged after it was disclosed that he had reported accidentally shooting himself in Glacier National Park in 2015. Mr. Sheehy said he had never revealed the wound in Afghanistan to protect those who served with him from an investigation into friendly fire and then lied about the incident in the park.