Weber joined Blair at a Scarborough burrito shop Thursday, where Blair officially launched his campaign, to formally withdraw and offer a public show of support.
"I want us to have the best chance possible of electing a Liberal this fall and that is why ... I have decided to drop out of the race and support Bill Blair as our Liberal candidate," Weber said in a statement posted to his website.
"I have come to know Bill Blair this past week, and I believe he is the best candidate we can put forward ... Scarborough Southwest has not had a candidate of his profile and credentials in many years."
Blair, who ended his tenure as Toronto's police chief in mid-April, announced his intention to run for the nomination on Sunday. The seat is currently held by New Democrat Dan Harris.
In an unusual move, Liberal Party Leader Justin Trudeau hosted Blair in Ottawa earlier this week, where the pair answered questions from media after Trudeau delivered a speech to a firefighters' organization.
Blair's intent to run for the Liberals surprised some observers.During his time as Toronto's police chief, he publicly endorsed policies championed by the Conservatives, such as mandatory minimum sentences and carding.
He told CBC News this week, however, that his values most closely align "with Mr. Trudeau and the Liberal Party."