UEFA's auction formally began last week and was expected to last for several months. However, Sky last night emerged as a "clear winner" in the initial stage. The purchase, estimated at costing £240m, includes rights to all Tuesday matches and all Wednesday matches except the first-choice fixture.
Another round of bids will be held for the first-choice Wednesday game and simultaneous TV rights (with Sky) to the tournament final. The BBC remains a favourite as it was rumoured to be "determined" to take some Champions League games.
Rights are currently shared between ITV and Sky.
UEFA said in a statement: "After the first round of bidding, BSkyB emerged as the clear winner for a number of rights packages... The rights will be widely exploited across all broadcast platforms ensuring significant audiences and exposure throughout the UK.
"By virtue of its commitment to industry-leading production standards and its unrivalled programming capacity, Sky Sports has proved to be an exceptional partner for the UEFA Champions League in the UK for a number of years."
The governing body added: "UEFA has received a number of offers for the remaining rights. However, the competitive nature of the bidding has been such that the award of these rights has yet to be concluded. UEFA has therefore invited a second round of bidding, and a separate statement in relation to the award of these rights will be made in due course."
Sky chief executive Jeremy Darroch said: "We have secured an excellent rights package at a price which we believe reflects their value to our customers and which recognises the increasing attractiveness of this competition to our business.
"The Champions League as a competition is going from strength to strength, as is the performance and contribution of English and Scottish clubs."
Vic Wakeling, Sky Sports managing director, added: "We have used digital technology over the last five seasons to offer a menu of live games. It has worked superbly and given viewers choice; they can decide which game to watch and they appreciate that. And we have introduced the exceptional quality of HD. This new deal means we can offer an even better service."