Mr Robert, who announced he would step down earlier this month, tendered his resignation on Thursday.
The resignation will trigger a by-election in his Gold Coast electorate of Fadden.
In a statement, a spokeswoman for House of Representatives Speaker Milton Dick said dates for the by-election were now being considered, with an announcement on the timing to be made soon.
Mr Robert was first elected to the seat in 2007 and served in roles including employment minister, skills minister and NDIS minister during the previous coalition government.
At the last election, Mr Robert suffered a 3.5 per cent against him.
The coalition holds the safe seat by more than 10 per cent.
Two candidates have nominated for LNP preselection - Gold Coast Council planning chief Cameron Caldwell and former Queenslander of the Year Dr Dinesh Palipana.
Party nominations for the seat close on Friday.
On Wednesday, Prime Minister Anthony Albanese said Labor was yet to decide if it would contest Fadden, saying expectations about winning the very safe Liberal seat were "realistic".
Mr Albanese had described Mr Robert's absence from parliament during the budget sitting - after the coalition MP had announced his intentions - as "completely unacceptable".
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