Brown was elected in a special election Tuesday to fill the unexpired term of the late Sen. Edward Kennedy.
The state's senior senator, John Kerry, told reporters his criticisms of Brown during campaigning were history.
Quoting the inscription Kennedy wrote on a photo, Kerry said, "Ted Kennedy wrote me, he said, 'As Humphrey Bogart would have said, this could be the beginning of a beautiful friendship.'"
Kerry said he looked forward to working with Brown, a state senator, on healthcare and other issues the Senate will consider.
"You have to work across the aisle here to make things happen. Americans don't just elect Democrats and Republicans, they elect people to be responsible with the people's business," Kerry said. "He'll have his chance to vote for Massachusetts many times over the next few years, and that will define him, not me, not him here today."
Brown said he he looked forward to working with Kerry in the future, as he has in the past.
"I have a great relationship with the delegation because of my years at the statehouse," Brown said.
Brown repeated a sentiment he said Wednesday: He's beholden to no one.
"I don't owe anybody anything," Brown said.
Kerry said he spoke with Senate Majority Leader Harry Reid about seating Brown as quickly as possible.
"I think seating Scott Brown as expeditiously as possible is important. We want to respect the election results. And nobody wants to try to delay this process," Kerry said.
Brown also visited Sen. Paul Kirk, appointed to the seat until the Tuesday's special election, as well as Senate Minority Leader Mitch McConnell, R-Ky., Sen. John McCain, R-Ariz., and others.