WASHINGTON—The Senate on Thursday approved the most extensive overhaul of financial-sector regulation since the 1930s, hoping to avoid a repeat of the financial crisis that hit the U.S. economy starting in 2007.

The legislation passed the Senate 59 to 39 and must now be reconciled with a similar bill passed by the House of Representatives in December, before it can be sent to President Barack Obama to be signed into law.

The...