Senators and their staff were shocked by Trudeau's announcement, which he made to them shortly before going in front of reporters to explain the move.
Trudeau said the country isn't ready for the years of constitutional debates that would likely be required to make the Senate an elected body or change its composition, but that this is one move he can make to try to bring down the partisan tone of the embattled institution.
James Cowan, who had been the party's leader in the Senate, says the formerly Liberal senators will continue to support Trudeau and call themselves the Senate Liberal caucus.
He says they are still the Official Opposition in the Senate and that he will continue to be their leader.
"They're still our friends and we share their values," he said about Liberal MPs.
"I think not a lot will change. I think that there is a perception perhaps that senators in our party and in the other party are under the control of folks on the other side. That's not been the case in our side. We obviously talk, consult with them and we have had the privilege of being part of their caucus up to now. We won't have that anymore. But we'll continue to talk to them and I suspect that not a great deal will change."
Cowan says Trudeau's move has nothing to do with an upcoming report by Auditor General Michael Ferguson, despite the accusation from Pierre Poilievre, the government's minister of state for democratic reform.
Poilievre alleged Trudeau suspects there will be bad news in the auditor general's report and is trying to pre-empt any criticism of the party.
Ferguson's office said on Twitter that no one has seen an advance copy of the audit report. Trudeau said none of the now-Independent senators had approached him about any possible problems with their expenses.
Cowan says the caucus will still have the power to discipline its members.
Newfoundland and Labrador Senator George Baker, who was named to the Senate in 2002, called it a fantastic announcement.
"It was an incredible surprise. A surprise to everybody, but it was something that Canadians have been asking for," said Baker, who was a Liberal MP from 1974 until he was appointed to the Senate.
"It is the most important announcement I think that's ever been made for the Parliament of Canada. The depoliticization of the Senate is one of the most important things that must take place at this moment in time."
Baker said he thinks the Conservative government will have to respond by making the same move.
Some senators took to Twitter to voice their support.
"Have [and] will always support Liberal values in Canada. To continue important work reviewing legislation for #PEI citizens [and] all [Canadians]," said Percy Downe, who was a chief of staff to former prime minister Jean Chrétien and named to the Senate in 2003.
"Mood upbeat in Liberal Senate caucus. Now we will serve Canadians more effectively," Mobina Jaffer said on Twitter.
Jaffer was appointed to the Senate in 2001 and was elected to two different roles on the Liberal Party's national council in the 1990s.