Large numbers of migrants have been making unsanctioned crossings on Roxham Road at the US-Canada border.
The move closes a loophole created by a 2004 asylum agreement with the US on where migrants have to make their asylum claims.
It prevented Canada from turning away people trying to enter at unofficial crossing points.
As a part of the deal, Canada will now also create a new refugee programme for 15,000 migrants fleeing persecution and violence in South and Central America, unnamed US officials told CBS News, the BBC’s US partner.
Mr Biden is in Ottawa, Canada, for 24 hours to talk about a series of economic, trade and immigration issues with Mr Trudeau.
The migration accord is scheduled to be announced before he returns to the US on Friday.
The agreement is expected to allow officials on both sides of the border to turn back such asylum seekers heading in either direction.
The US side has also seen a rise in migrant crossings there from Canada with the decision.
The move is part of efforts to limit an influx of migrants at Roxham Road, an unofficial crossing between New York state and the province of Quebec.