Trudeau said his agent at the time, Speaker's Spotlight, paid for the flight but that an invoice was "inadvertently" sent to his MP's office and he was reimbursed for the amount, due to a "human error" by his staff.
All MPs are allowed 64 travel points per year, with one point worth a return flight.
“Shortly after being advised of this error, I wrote a personal cheque for the improper claim of $672 and asked that it be delivered to the Receiver General for Canada immediately," Trudeau wrote in a statement placelined Thornhill, Ont., where he is scheduled to speak Thursday afternoon.
Trudeau added that this event led his office to conduct a review of his expenses and two more improperly billed invoices were discovered.
"One is from Nov. 6, 2009, for $83.55, and the other is from May 7, 2010, for $84.50. While I was travelling on those days, the main activities that I undertook were related to contracts with Speaker’s Spotlight and my return home to Montreal. As such, I have reimbursed the Receiver General $168.05," Trudeau wrote.
He added that if the system of proactive disclosure his MPs are now using to publicize their expenses was in force earlier, the "errors" could have been caught sooner.
Trudeau ordered his caucus members, including senators, to post their travel costs for each trip, and any hospitality expenses, starting last fall. So far, expenses have been posted for only the fiscal quarter ending in September 2013.
Conservative MPs adopted a similar system in December, although their postings are more up to date.
Last year, after a Saint John-based charity revealed it lost money on an event after paying a $20,000 speaking fee to Trudeau, he offered to pay not only the charity's money back, but any organization he'd billed for speaking appearances since he was first elected.
He also pledged not to charge for any speaking engagements in future as long as he is an MP.