Adams’ last competitive game in charge brought a play-off final victory against Newport County AFC at Wembley, putting Morecambe into the third tier for the first time.
Managers including Keith Hill and Phil Parkinson were the initial favourites with the bookies but Robinson was the board’s choice, agreeing a three-year contract.
“It’s an exciting challenge,” he said.
“It’s the first time in the club’s history it’s in League One, it’s exciting and it (the move) all happened very quickly.
“I spoke to the chairman on Friday, came down on Saturday and I was very impressed with what people were telling me.
“I had a lot of questions for them (the board), they had a lot of questions for me. It all happened really quickly and we agreed to come down and take the club forward.
“This season, they have come to the fore and Derek has done a terrific job.
“We have to use that momentum, build on that, and that’s what I aim to do.”
After a short spell in League One with Oldham Athletic in 2016/17, Robinson attracted attention with the job he did at Motherwell.
Having taken charge, initially on an interim basis, in February 2017, he had two full seasons which saw them finish seventh and eighth in the Scottish top flight.
The first of those seasons saw them reach both domestic cup finals, while his third campaign - curtailed as a result of the pandemic - ended with Motherwell in third reaching the Europa League qualifying stages.
With Morecambe now readying themselves to face teams who have played Premier League football, Robinson believes they have plenty in common with his last employer.
He said: “I think there are a lot of similarities, it’s a club where expectations have traditionally been a bit lower and they have overachieved.
“It’s been shown in the past with Motherwell when we got to two cup finals, finished third and got to Europe: there’s no reason why Morecambe can’t be similar to Motherwell.”
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