Via the Associated Press. It's apparently a major-league deal worth about $15 million. Second overall pick Dustin Ackley has also apparently signed. This rules out a couple possible options for the Bucs in next year's draft. Despite all the drama, it should be no surprise that Strasburg signed; it doesn't seem possible that his stock could ever get higher.
I have no confirmed information about any other Pirates picks who may have signed just before the midnight deadline. The Post-Gazette reports that the Bucs spent the most money of any team in the N.L. Central.
Here's my report after seeing Strasburg pitch in March.