The Victorian senator appeared briefly in the Senate chamber on Monday as parliament returned from a five-week break.
He resigned from the Liberals in June after allegations about his behaviour were made by independent senator Lidia Thorpe and former Liberal senator Amanda Stoker.
He has denied all the allegations raised against him.
Claims of inappropriate conduct have also been made by a third unnamed person.
Opposition Leader Peter Dutton has called on Senator Van to resign from parliament, but the Victorian senator quit the party before a committee could meet to discuss the allegations against him.
Mr Dutton said he hoped the expulsion sent a "very clear message" about what was expected from parliamentarians.
In a letter to Victorian Liberal Party president Greg Mirabella, Senator Van said he could not remain a member of a party that "tramples upon the very premise on which our justice system is predicated".
Separately, Mr Dutton voiced support for party colleagues facing preselection challenge before the next election.
His deputy Sussan Ley and backbencher Melissa McIntosh could lose their seats if local challenges against their candidacy are successful.
"I've given strong letters of support to each of my colleagues who have asked for it," he told reporters in Canberra.
"I'll provide whatever support is needed to my colleagues - Sussan Ley, obviously is deputy, and Melissa, who's done a great job and is a very popular local member, and similarly other colleagues that might be challenged."
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