The floor at Newport Library was left sodden after torrential downpours descended on the region towards the end of May.
The building was shut for the whole of last week. Carpet covering much of the ground floor building had to be replaced, but staff were thankful that no books or other equipment was damaged.
Telford & Wrekin councillor and Newport's mayor Peter Scott welcomed back what he called a vital service for the town.
He said: "I'm really relieved it has reopened, as it is a facility we simply couldn't do without.
"What the temporary closure has shown is how much we depend on the library, not just for the books but for all the other vital services they offer there.
"There is the FirstPoint for blue badges, the internet access, the service for reporting problems to the council.
"It's very much a focal point for the town and I'm glad it is open again."
The staff at at the library said that they were pleased to get back to normality.
Kirsty Sinchett is the Team Leader at Newport Library.
She said: "It was horrible at the time, there was so much water pouring through the library roof."
Telford and Wrekin Libraries uploaded a shocking video to their Facebook page, showing water pouring through the ceiling.
The video shows several buckets positioned to catch some of the rain water, with little success against the downpour.
Kirsty added: "We've had to have the carpet replaced as well as some new ceiling tiles. And of course we've also had to let the ceiling and floors dry out after the all the flooding.
"Our customers have been really supportive during our closure, and we've even received flowers and biscuits from our lovely regulars. We've been quite busy this morning so far, it's good to get back to business as normal."