Profits will fund improvements for the town centre.
The 32 shops at Fleet Walk include some of the top high street names including TK Maxx, Sports Direct, JD Wetherspoon and Starbucks.
It is understood the centre management has had interest from businesses in the three currently empty units.
The purchase of the centre was made under the council’s £100m Economic Regeneration Fund created this year.
The current management team is expected to stay in place.
Fleet Walk forms a key part of Torquay’s shopping centre and the council aims to use its ownership to support the vitality of the area by improving the offer and attracting more visitors.
The high street has suffered from the departure of big names, with New Look leaving in April and H&M announcing its store in the former Woolworths building was for sale and expected to close.
The switch to more leisure use received a boost in August when Merlin Cinemas was given planning permission to convert the empty former BHS store in Union Street into a new 13-screen cinema.
Other regeneration schemes under way include the £32m redevelopment of Torwood Street near Torquay Harbour.
The project will see the creation of a 130-bed Hilton Hotel, new offices, bars and restaurants.
Torbay Council is funding the £11m build of a Premier Inn hotel on The Terrace car park above the harbour.
Work has started to prepare the site ahead of the main construction work on the six-floor 120-bed hotel.
Along the seafront, the council is working with tenant the Venus Cafe on plans to convert the empty Old Toll House into a restaurant and bar.