Towcester was placed into administration in August last year and was sold to Fermor Land LLP, a company with links to owner and racecourse chairman Lord Hesketh.
While the track's fixtures have been run elsewhere since then, it had been hoped either ARC or The Jockey Club would step in to run the venue - but that possibility has now been dashed.
A statement from ARC read: "Arena Racing Company ("ARC") can confirm that, following the closure of Towcester Racecourse, ARC has purchased the unencumbered freehold of the 10 fixtures that remained within the ownership of Fermor Land LLP.
"The transfer of these fixtures from Fermor Land LLP to ARC has been approved by BHA, with two to still be staged in 2019. The host venues for the fixtures on Thursday 28 November and Thursday 19 December will be confirmed shortly, with the location of the 10 fixtures scheduled in 2020 to also be confirmed in due course."
Richard Wyman, chief operating office for the BHA, said: "We are saddened to see the closure of Towcester, a popular racecourse which will undoubtedly have created fond memories for many racing fans and participants.
"We had hoped, following the course going into administration in August 2018, that the new owners might find a solution which allowed for racing to resume at Towcester, and it is disappointing that has not proved possible. The BHA will now work with ARC to find the most suitable venues for the 10 fixtures involved, which will all remain over jumps.
"From championship racing to grassroots, jump racing remains extremely popular, with a growing base of loyal and knowledgeable supporters. The outlook for the sport is a positive one, and we will continue to work with parties across the industry to ensure that jump racing in Britain goes from strength to strength in the future."
Racing first took place at Towcester in 1876, and almost 140 years later it was the venue for Sir Anthony McCoy's 4,000th winner - when Mountain Tunes was roared home in 2013.
