The Prime Minister said Lord Roberts, who was a Welsh Office minister in the Thatcher and Major governments, "did so much for Wales".
Welsh Secretary David Jones said the peer, who as Wyn Roberts was MP for Conwy from 1970 until 1997, was "arguably the greatest Welshman of his generation".
Writing on Twitter Cameron said:
I'm sad to hear a great Conservative, Lord Roberts of Conwy, has died. He did so much for Wales, including piloting the Welsh Language Act.— David Cameron (@David_Cameron) December 14, 2013
Jones added his tribute on the website, saying: "Wyn Roberts was arguably the greatest Welshman of his generation; a wise man and a kind and good friend."
Huw Jones, chairman of the S4C Authority, said former journalist Lord Roberts was a "guardian angel" for the Welsh language broadcaster.
He said: "Wyn Roberts was a guardian angel for the Welsh language and for S4C within the Conservative government of the 80s and 90s.
"Both were close to his heart and he did everything he could to promote and support them. His close interest continued when he became a member of the House of Lords and his wise counsel was priceless.
"Alongside his measured and careful style, he had humour and mischief in his eye and great personal warmth. He made a huge contribution at a critical time for the Welsh language and he will be greatly missed."