The deal will boost Yahoo!'s online music offerings and is the latest in a string of deals between internet music sites and media companies desperate to increase their hold on the market.
Launch's shares shot up 50% to 91 cents (65p) on the news, while Yahoo!'s shares rose to $19.67 (£14) during early trading.
A Yahoo! subsidiary will acquire all of Launch's outstanding shares for 92 cents (65p) a share, and will extend a $3m (£2.1m) short-term security debt financing.
Launch is a free website that offers video-on-demand to its 4m users. Co-founders David Goldberg and Bob Roback will remain with the company but it is not known whether any of the company's other 175 employees will be made redundant.
In a separate announcement, Launch said it has settled a copyright infringement suit brought by Vivendi Universal's Universal Music Group. Launch agreed to pay for past performances and signed a license agreement to use Universal's recordings.