Mike Ashley's Sports Direct had bought a stake in Debenhams earlier this year before offloading it then putting in place a put option giving it the chance to take a larger holding.
The two companies had previously indicated they were exploring opportunities to work together.
Mr Ashley, owner of Newcastle United and a shareholder in Rangers, has been diversifying the company he founded in recent years including snapping up fashion retailers Cruise and USC from Sir Tom Hunter and his West Coast Capital investment vehicle.
Yesterday Debenhams confirmed it was opening the concession to improve "underperforming" areas in its stores.
Sports Direct will open in Debenhams in Harrow and Southsea along with Costa this month although the coffee chain will also be in Derby, Exeter, Haverfordwest and Woking.
Sportswear is thought to represent less than one per cent of the total sales at Debenhams.
The department store owner said it is in discussion with a number of other brands over more concessions.
Like-for-like sales grew 0.7 per cent in the 41 weeks to June 14 with gross transaction value rising 1.4 per cent and online sales up 18.8 per cent over the same period.
The company said it had seen an improvement in margins in the second half of the year after limiting promotional activity and starting its summer sale two weeks later than in 2013.
Internationally its Danish arm, Magasin du Nord, and its franchise business were said to have performed well and offset continued weakness in Ireland.
A £200m bond issue is planned to take advantage of "attractive credit markets" while banking facilities are being extended to 2018 for a similar reason.
Debenhams has 158 stores in the UK with 14 of those in Scotland. Shares closed down 1.3p, or 1.8 per cent, at 70.8p.