Trump praised the team for their playoff run and their "spectacular victory" in the World Series against the Los Angeles Dodgers during a ceremony on South Lawn of the White House.
"Each Red Sox player is a shining example of excellence living out an American sporting tradition that goes back many generations," Trump said.
"Through every pitch, inning, game and series the 2018 Red Sox never gave up and never backed down, always played like champions."
Right fielder J.D. Martinez thanked Trump for his hospitality and presented him with a commemorative jersey bearing the president's last name. He also poked fun at Trump for being a fan of their rivals, the New York Yankees.
"I know celebrating a Red Sox victory is tough for you," Martinez said.
About a dozen players -- and manager Alex Cora -- skipped the event. The NBA champion Golden State Warriors declined an invitation after winning the title in 2017 and the 2018 NFL champion Philadelphia Eagles did the same.
Prior to the White House ceremony, the team visited veterans at the Walter Reed National Military Medical Center.
"What an honor to spend our morning with you!" the club said in a tweet.
Trump also offered to guide the team on a tour of the Lincoln bedroom.
"They never get to see the Lincoln bedroom ... You're not supposed to be showing it," he said. "So, if the press, the media doesn't report me for this, I'm going to take them up and show them the Lincoln bedroom."