BlackRock confirmed the news early Wednesday. Shares of JPMorgan rose 1 percent as the broader market rallied and the Dow Jones industrial average topped the 20,000 milestone for the first time.
A State Street spokeswoman told CNBC that the firm will still retain custody over some of BlackRock's assets.
"We remain a significant service provider for BlackRock, and the transition will not be fully completed until 2018," she said. "As I'm sure you've seen from our earnings announcement, we continue to see strong client demand for our services with new asset servicing wins of approximately $1.4 trillion for 2016."
On Wednesday, State Street reported fourth-quarter earnings that beat analysts' expectations, although its revenue missed. Its sales of $2.53 billion marked a 0.31 percent decline from the year-ago period.
As of yesterday's close, State Street shares are down 1.6 percent for January.