The former UUP leader’s passing was announced on Monday evening.
Foyle MP Mr Eastwood said: “David Trimble’s life has left an indelible mark on our shared island’s story. Over the course of his political career but particularly in difficult years of the Good Friday Agreement negotiations he demonstrated immense courage and took political risks that sustained the life of our fledgling peace process. He doesn’t often enough get credit for it but without David Trimble’s fortitude, there would simply have been no agreement.
“The image of David and Seamus Mallon walking through Poyntzpass together in 1998 to comfort the families of Damien Trainor and Philip Allen is an enduring icon of the peace process that inspired a whole generation of people who wanted, and needed, to believe that our shared future could be different from our divided past. It is my enduring memory of his commitment to reconciliation.
“My thoughts and prayers are with Daphne, Richard, Victoria, Nicholas and Sarah at this difficult time. I hope they are comforted by the immense legacy that David left to the people of Northern Ireland.”
The Taoiseach’s statement said: “I wish to express my deepest condolences to the family, colleagues and friends of David Trimble. He played a key role as leader of the UUP, and his was a long and distinguished career in Unionist politics and in the politics of Northern Ireland.
“All of us in politics at the time witnessed his crucial and courageous role in the negotiations leading to the Good Friday Agreement and his leadership in building support in his party and his community for the Agreement.
“Fittingly, his contribution was recognised internationally and most notably by the awarding of the Nobel Peace Prize to himself and John Hume ‘for their joint efforts to find a peaceful solution to the conflict in Northern Ireland’.
“As the first First Minister of Northern Ireland he began the arduous work of bedding down the Executive and delivering for the people of Northern Ireland. In his speech accepting the Nobel Prize, Trimble spoke about the ‘politicians of the possible’, a phrase which I think sums up the David Trimble we all knew, and it speaks to his achievements over many decades, often in challenging circumstances.
“The work of reconciliation begun in the Good Friday Agreement continues, and as new generations pick up the mantle of this work, it is fitting that we pay tribute to Lord Trimble for his central contribution in setting us on the path to peace and reconciliation.”