Mr Robinson, 66, made the widely-expected announcement in an article in the Belfast Telegraph.
He will not contest next May's Assembly election and said he is likely to leave office in the coming weeks.
"He was one of the best political strategists we have in Northern Ireland," said the DUP MP and Christian Jim Shannon in an interview with Premier.
He added: "He had that ability to have long term vision when it came to seeing where we were going. It wasn't always a short term reaction to what was happening, he had a vision for the future."
There had been growing speculation Mr Robinson would outline his departure plans at the DUP's annual conference this weekend.
In the event, he confirmed his exit in a pre-conference interview with the Belfast daily paper.
"I think it would be disrespectful to the party membership if I was to go through a conference with the pretence that I would be leading the party into the next election," he said.
"I think they have a right to know what the circumstances are."
The Christian MP for North Belfast Nigel Dodds will be among the favourites to take over as DUP leader.
However, with Mr Dodds based in Westminster, another senior party figure may take on the role of Stormont First Minister.
Current Finance Minister Arlene Foster has been touted as a potential leader of the power sharing coalition.
Mr Robinson suffered a heart attack earlier this year but he has insisted he had already made his mind up to leave before the health scare.
Mr Shannon told Premier: "Perhaps he thinks he, and I believe he has, done his bit and it's time now to move on.
"He is, if I can say it with respect, in the retirement age, and maybe it's a good time to go and spend time with wife and family."
DUP MP and Christian Jim Shannon speaking to Premier's Antony Bushfield: