"I'm sick and exhausted of you guys", Gianforte said in audio of the event released by The Guardian.
"I'm going to let the people of Montana decide who they want as their representative", the Speaker told reporters.
Gianforte beat Democrat Rob Quist, a banjo player and first-time candidate who had focused his campaign on criticism of the Republican effort to repeal and replace former President Barack Obama's health care law.
Rep. Steve Stivers, chairman of the National Republican Congressional Committee, hailed Gianforte's win.
With 301,231 votes counted, Gianforte was up 50% to 44% with an edge of 151,021 votes to 132,555 for Quist, according to the Secretary of State website.
At his victory celebration, Gianforte apologized to Jacobs by name.
Gianforte's victory is a boost for Republicans, who are anxious Trump's political stumbles and increasing unpopularity may cost the party its House majority in 2018 elections.
Thursday's election leaves Democrats without a win in special elections since November, with Republicans having won contests in Louisiana, Kansas and now Montana. "That's the Montana way", he told his supporters.
Jacobs was the reporter Gianforte allegedly body-slammed to the floor.
It was unclear if Gianforte's assault had an impact on the vote. Party strategists argued that Gianforte's margin in a state where Trump swamped Hillary Clinton by 20 points bodes well for dozens of other districts where the parties are more evenly matched. And the president, in Italy for a G-7 summit, said to journalists after Gianforte's victory: "Great win in Montana".
In Washington, Republican lawmakers reacted to the situation.
Gianforte specifically addressed his apology to Jacobs.
"Last night, I made a mistake", he said, to more laughter, "I took an action that I can't take back".
"No, please", he said as he raised a hand to supporters so he could continue. He campaigned last weekend with Sen. The Gallatin County Attorney is also reviewing the case to see if additional charges are merited.
Sheriff Brian Gootkin announced in a press conference Wednesday night that after conducting an investigation and interviews, "there was probable cause to issue a citation to Greg Gianforte for misdemeanor assault". Plus, could anyone really say no to free pizza?