Farquhar led the Blue Jays' Minor League system in 2009 with 22 saves. He will report to Triple-A Las Vegas.
Purcey, who was out of options on his contract, was designated for assignment by the Blue Jays on Tuesday. The club had 10 days to either trade, release or waive the Illinois native, and general manager Alex Anthopoulos maintained all along he was confident a deal would get done.
The 28-year-old Purcey pitched 1 1/3 scoreless innings against Oakland earlier this season. That was enough to convince the Athletics he would be worth taking a chance on.
"He had one bad outing the other night, but he pitched well against us, and we feel like he has a chance to contribute in the 'pen," A's assistant general manager David Forst said.
The trade marks a disappointing end to Purcey's career in a Blue Jays uniform. He arrived to the organization with high expectations after being selected in the first round of the 2004 First-Year Player Draft.
Purcey failed to live up to the hype and battled control problems for most of his career. He went 5-10 with a 5.42 ERA and 78 walks over 149 1/3 career innings.
With a crowded bullpen, the Blue Jays felt they could no longer hold a roster spot for Purcey while he worked through his struggles.
"We had tried to find ways to use him, be productive, gain some consistency," manager John Farrell said recently. "I know that there is a long history with a lot of attempts with him.
"It's a very tough decision when you consider the person and the fact that he was a high Draft pick here, but I think at some point that becomes performance-related rather than status-related."
Gregor Chisholm is a reporter for MLB.com. Read his blog, North of the Border, and follow him on Twitter @gregorMLB. This story was not subject to the approval of Major League Baseball or its clubs.