The 63-36 vote on the bill Thursday night was carried by moderates in both parties; the legislation now goes to President Biden to sign.
Banks' interest is growing in the evolving technology of artificial intelligence and its likely impact on their business.
The deal now heads to the Senate, where approval is virtually certain; Senate GOP leader Mitch McConnell said the measure could be voted on as soon as Thursday.
The bank aims to almost double its profit from wealth management through asset growth, more lending and expanding markets, co-president Andy Saperstein said at a conference.
The settlement with the SEC follows Carrie Tolstedt's agreement in March to plead guilty to obstructing a problem of the bank's practice of opening accounts for customers without their authorization.
The unit, called 23 Wall, is led by JPMorgan veteran Andy Cohen and focuses on about 700 families worth more than $4.5 trillion.
The measure seeks divestment of an estimated $15 billion from oil and gas companies by CalPERS, CalSTRS.
Legislators have less than a week to approve the agreement before the default deadline next Monday, June 5.
About $46.7 billion poured into US money market funds in the week ended Wednesday as investors piled into assets offering relatively safer returns amid the uncertainty around talks on extending the US debt limit.
The bank offered full-time or transitional roles to almost 85% of the nearly 7,000 employees still working at First Republic when it collapsed, and told the rest they wouldn't get offers.
