The Irish Rugby Football Union confirmed on Friday they had been informed Sexton would not be renewing his contract with them to remain playing full-time in Ireland from the end of this season, and Leinster coach Joe Schmidt said the offer Sexton had received was "exceptional, even by French standards".
It is thought that Sexton will become the latest big-money signing for Paris-based Top 14 club Racing Metro.
Sexton, 27, has won 34 caps and is a firm favourite to be the British and Irish Lions Test fly-half against Australia later this year. He also played a key role in Leinster winning three European titles in the last four seasons, starring when they won finals against Leicester, Northampton and Ulster.
In a statement, IRFU chief executive Philip Browne said: "We are very disappointed, as we know the Irish rugby public will be, that Johnny Sexton will not be playing his rugby full-time in Ireland from next season.
"Johnny is a major talent and his full-time presence in Ireland will be missed, particularly by Leinster. We wish Johnny continued success with his career and he will receive all the support he needs over the next number of weeks in what we know was a very difficult decision for him.
"While we remained in the fight right up until the last possible moment to keep Johnny in Ireland with a very strong offer, ultimately, following negotiations with the player's agent, we had no option but to take the decision that it would not be in the best interest of Irish rugby to chase the reported financial incentives being offered.
"The IRFU has made a commitment to, and been largely successful in, keeping as many Irish players as possible playing full-time in Ireland.
"However, we have always recognised that some of our players will be targeted by overseas clubs with offers which, quite simply, are not within our orbit.
"While Johnny has made the decision to move on to a new club, the IRFU is fully committed, together with the provinces, to maintaining its programme of nurturing and retaining Irish rugby talent. We feel that the benefits of the careful and considered management of those players will allow us to maintain this policy."