EBay Inc. has agreed to pay up to $4.1 billion to acquire Skype SA, a Luxembourg-based startup with just $7 million in revenue last year, giving the Internet telephony provider’s American venture backers an apparent huge payback.

The move is intended to broaden the online auctioneer’s portfolio of service offerings and help drive growth, said San Jose, Calif.-based eBay, amid pressure to spur growth and diversify its businesses in a rapidly maturing industry. EBay said it will combine Skype with its core online-auction business and PayPal Inc. payments-processing service that will create an enhanced system for doing business on the Internet.