Sexton, who has won 34 caps and is favourite to be the Lions' Test fly-half during their summer tour to Australia, has signed a contract, described by Joe Schmidt, the Leinster coach, as "exceptional, even by French standards". It is thought to be worth £640,000 per year over two seasons.
"We are disappointed – as we know the Irish rugby public will be – that Johnny will not be playing his rugby full-time in Ireland next season," said Philip Browne, the IRFU chief executive.
Sexton is the first regular Ireland internationalist to succumb to the riches on offer in France, with the IRFU having previously been successful at retaining their top players.
Brian O'Driscoll was been linked with French clubs while Jamie Heaslip, the national side's new captain, last year rejected several offers to stay at Leinster.
Sexton's departure places Ireland in the same position as Wales and, to a lesser extent, England, who have lost internationalists to the vast spending power that exists overseas.
The IRFU admitted the sums involved forced them to withdraw from negotiations, stressing the money would be better spent elsewhere. "We remained in the fight right up until the last moment to keep Johnny in Ireland," Browne said.
"But, ultimately, we had no option but to take the decision that it wouldn't be in the interests of Irish rugby to chase the financial incentives that are being offered overseas."