The final deal, which includes 342 acres, a drag strip, a road course and an oval racing track, will total $2.06 million after a 10 percent auction buyer's premium.
The closing is scheduled to take place within 30 days.
"We're happy to see it move into the hands of someone who is going to operate it for the fans down there," Dover CEO Denis McGlynn said Wednesday.
"It's a happy end for a story for everybody down in Memphis, and I wish them the best of luck."
Dover previously had Memphis Motorsports Park listed with Colliers International, a commercial real estate firm, for $6 million.
Jason Rittenberry, the former CEO of Memphis Motorsport Park and current CEO of Moroso-owned Palm Beach International Raceway, said the Memphis racetrack will need $1.5 million-$2 million in capital improvements to get it ready to host major events.
"Yes, I feel like we got a good deal on the land, but it's not the steal everyone thinks we got," Rittenberry said, noting that equipment, furniture and fixtures were sold off separately at Tuesday's auction.
Negotiations for the facility between Moroso and Dover been have under way for the last six months, Rittenberry said, but the parties were unable to agree.
A previous offer, he said, was significantly more than Tuesday's winning bid. But that offer included all of the facility's assets, including trucks, tractors and food equipment, which Moroso will now have to buy.
Rittenberry said he spent $30,000 on such items at Tuesday's auction, but the facility will need much more.
He said he hopes to announce several national International Hot Rod Association drag-racing events in the coming days or weeks.
"Obviously we've had great success with this same group at Palm Beach International Raceway," said IHRA president Aaron Polburn.
"Memphis is a great market, and I can't wait to get the ball rolling and start getting IHRA events at the facility."
Moroso will host an Outlaw Monster Truck Spectacular event at MMP on Sept. 17.
Moroso is in talks with several sanctioning bodies that want to race on the facility's three-quarter-mile oval track, but Rittenberry said nothing is firm for the course in 2011.
It also remains to be seen whether any NASCAR-sanctioned event will return to Memphis.
"We'll have conversations with them, but I'm not sure yet about the viability of bringing NASCAR back to Memphis at this point," Rittenberry said. "I can't guarantee today what the future of NASCAR in Memphis will hold."