Council bosses say that the site, which has been earmarked as being part of a huge redevelopment project, is “no longer commercially viable” to keep open in the short-term.
The centre has been run in recent times by Everyone Active on behalf of the council.
The company charged with revitalising the Seaburn area is Siglion, which hopes to create new housing, seaside retail and leisure facilities in the coastal community.
It revealed earlier this year a proposed masterplan to improve the area.
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The firm has said it hopes to make Seaburn a "distinctive, popular and first choice destination to attract visitors and families from the city and across the region to live, work and visit".
Chiefs have said they hope to put Seaburn "on the map as a great destination for all age groups, and boost its reputation as a fantastic 21st century seaside attraction".
Coun George Howe, who serves Fulwell ward, said he agreed with the closure plan but wants to see something to attract more people to Sunderland built in its place.
"I think it’s time it was closed," said Coun Howe.
"I’ve been campaigning for a swimming pool to be built on the site and hopefully that will happen.
"We need something there that families will use all year round to get visitors coming regularly, not just something that’s used on certain months.
"We don’t need any more shops, in my opinion."
Confirming the closure plans for the Seaburn Centre, Coun Mel Speding, the city council’s cabinet secretary, said: "The city council’s masterplan for Seaburn, adopted in 2011, identifies the area, including the Seaburn Centre, for comprehensive redevelopment.
"To date the centre has been operated on a short-term basis by Everyone Active (the council’s leisure partner) pending the long-term redevelopment of the site
"It is no longer commercially viable to keep the centre open on a short-term basis and, therefore, it will close to the public on Sunday, March 26, 2017.
"The long-term plans remain for the wider redevelopment of this area."
The Seaburn Centre has in recent times hosted science fiction fairs, State of the City debates and the city’s Festival of Remembrance concert as well as walking football sessions.
Ian Bradgate, Everyone Active’s contract manager, said: “It is important to Everyone Active that we offer support for colleagues, user groups and members that will be effected by the closure of Seaburn Leisure Centre on March 26, 2017.
"We are currently liaising with the centre’s colleagues on the matter and are working with our user groups and members to move their activities to our other centres. Our other centres in the area include Sunderland Aquatic Centre, Silksworth Community Pool, Tennis and Wellness Centre, Silksworth Sports Complex and Ski Slope, Hetton Community Pool and Wellness Centre, Houghton Sports and Wellness Centre, Bunny Hill Wellness Centre, Raich Carter Sports Centre and Washington Leisure Centre.
"We invite people to email our colleague, Steve Dougal, on [email protected], with any queries they may have about the closure of Seaburn Leisure Centre."
John Seager, chief executive of Siglion, said: "We have been made aware by Sunderland City Council of their plans to close the Seaburn Centre next year. This decision is one they have made as a separate organisation.
"Siglion has a vision for the long-term redevelopment of the seafront, which will maximise the potential of an area that we believe is the jewel in Sunderland’s crown, seeing it developed and protected for future generations.
"We have applied for planning permission to create a mixed-use site, of which the provision of leisure activity is a key element.
"Siglion enjoys an open dialogue with Seaburn’s communities and perhaps this announcement provides us with an opportunity to engage further with the people of the area to learn how we can improve upon the area’s current level of leisure facilities in our ambitious regeneration plans for the area."