The pool matches would be shared equally, both will show two quarter-finals each, one semi-final each and the Final would be broadcast by both live. The four-year agreement is subject to contract.
Simon Green, director of BT Sport, said: "It is fantastic news for rugby fans that we have reached a deal with Sky Sports.
“The game of rugby had to come first and both companies have recognised that by showing a high degree of maturity and flexibility.
“We are delighted with the deal that has been struck and are hugely excited about bringing live action from both tournaments to our TV customers.”
Barney Francis, managing director of Sky Sports, said: "This is a good day for rugby. The agreement offers clarity for European rugby and enables the clubs to plan for the future. With these new competitions, we're delighted our viewers can look forward to even more top-class European coverage across our platforms.”