Total Fitness, which had gyms in Castleknock, Malahide Road and Sandyford, shut down without warning in March 2011.
Hundreds of members who had paid annual fees were left in the lurch by the closure. More than 100 people also lost their jobs.
The new development will consist of 3,116 square metres of shopping space on the ground floor and a 1,406 square metre health and fitness club on the first floor.
Tesco, which has an outlet in the adjoining shopping centre, had objected to the plans, saying the retail side of the development was not warranted because there was an abundance of shops nearby.
Tesco appealed to An Bord Pleanala, but it ruled in favour of the applicants Mardown Ltd. A board inspector said the location of the site beside the Clare Hall centre was favourable, as the new scheme would "complement and extend" the range of local facilities.
The plans include a 388 square metre restaurant on the ground floor and a new medical centre.
Albert Gubay is listed on planning forms as a director of Isle of Man-registered company Mardown.
The businessman, whose mother came from Co Clare, began his career selling sticks of rock to tourists in Wales before moving into the supermarket business.
Mr Gubay sold Irish and UK fitness chain Total Fitness to UK venture capital firm L&G in 2004.