The golden-clad building, home to a 25,000-book library, Telford & Wrekin Council's customer First Point and a Costa Coffee outlet, is the latest attraction to open at the much-heralded £250 million development in the town centre.
The new Southwater Library saw 8,500 visits in the second week, bringing the total amount of visitors to nearly 15,000 in the first fortnight.
Council chiefs said visitors to the library had borrowed 7,800 books since Southwater One opened and 450 children had joined the Summer Reading Challenge.
They say a total of 1,437 customers have also been helped by staff in the relocated First Point customer contact facility during the first two weeks.
Work is continuing on the rest of the development with both the 11-screen Imax Cineworld and the 85-bedroom Premier Inn hotel due to open next month. A string of restaurants, including Pizza Express, Harvester, Chimichanga, Zizzi, Bella Italia, Nando's and Wagamama are all scheduled to open later this year.
The second phase of Southwater, due in the next four to seven years, will see another 350 spaces added to the multi-storey car park.
There will be more bars, restaurants and shops on the ground level as well as homes and an extension to The International Centre.
Council bosses say their vision is that in eight to 15 years there will be more commercial ventures, homes and offices to create a "beating heart" to the town where people live and socialise. Councillor Kuldip Sahota, leader of Telford & Wrekin Council, said: "These latest figures demonstrate how Southwater is capturing the imagination of residents and visitors alike.
"The town centre is thriving on the renewed investment and interest in it."
The Southwater Library is staffed between 10am and 6pm Monday to Friday, 10am to 4pm on Saturday and 10am to 4pm on Sunday until September 30. A self-service facility is available in the library at other times when the Southwater One building is open.
On the ground floor, First Point offers access to a number of council services alongside partner agencies such as The Prince's Trust, the Royal British Legion, armed forces charity SSAFA, Citizen's Advice Bureau, the Red Cross and the Healthy Lifestyles Hub.