Former Connacht and Northampton Saints lock Browne, makes the move back to Ireland from Brive where he has made 13 European appearances in three season.
Commenting on the new deals Leinster Coach Joe Schmidt said: "We are delighted to announce the signings of two Irish qualified players in Damian and Fionn and we believe that both players have the potential to make an impression over the coming season.
"I know how enthusiastic both players are about linking up this summer, in Fionn's case his arrival will be a homecoming of sorts as he is a graduate from the Leinster Academy.
"Richardt has been a key performer in the Leinster front row this year and his contract extension is a further boost in addition to other recent contract extensions. With the extensions and new contracts for the younger players it is important that we continue to retain our best underage talent from the Leinster Academy."
In a further boost to Leinster, hooker Richardt Strauss has extended his contract until 2013 and Dominic Ryan has signed a new two-year deal.
Centre Brendan Macken and out-half Ian Madigan have extended their current deals while half backs John Cooney and Ian McKinley have both also signed their first professional deals with the province.