The sale was formally approved at the MLB quarterly owners' meetings in Minneapolis. The ratification marks the end of a months-long struggle that Ryan and Greenberg endured to take control of the club. Ryan will remain team president.
The group initially agreed to buy the team from Tom Hicks in January. But a messy bankruptcy case ensued and Ryan and Greenberg ultimately had to win a bidding war with Dallas Mavericks owner Mark Cuban to secure the franchise.
Ryan and Greenberg beat out Cuban with a bid valued at $590 million.
Commissioner Bud Selig said the Greenberg-Ryan group had "demonstrated an unwavering commitment" to the Rangers.
"I am confident that Chuck, Nolan and the entire ownership group will serve as dedicated stewards of this club by building a long-term, stable franchise," he said. "I am glad that the Rangers' great season on the field will get the attention it deserves during the pennant race."
Texas has a 7½ game lead in the American League West, the largest in any division in the majors.
With MLB's blessing, the team's assets will now be sold to the Greenberg-Ryan group, and the Rangers will officially emerge from Chapter 11 bankruptcy protection.
The Rangers' plan and sale to the Greenberg-Ryan group had been in jeopardy since shortly after the team's bankruptcy filing in May. Angry creditors successfully argued to re-open the bidding although the Greenberg-Ryan group was chosen as the team's owner in January after the original sale process.
Had the plan had been rejected, the team would have remained in bankruptcy court and the Greenberg-Ryan group - long endorsed by Major League Baseball - would have lost its chance to purchase the team, since its funding guarantee expired Thursday.
But after nearly three months of arguing attorneys, surprise lawsuits and even two-last minute attempts by Greenberg-Ryan to stop the auction, the group ended up with a winning bid that was about $100 million more than its opening offer.
Rangers attorneys say all disputes with lenders and others had been resolved, including an objection filed by Alex Rodriguez over concerns that he and other former players may not get the millions that the Rangers owe them. The Greenberg-Ryan group's winning bid includes paying more than $200 million to unsecured creditors - including A-Rod, who is owed $24.9 million in deferred compensation six years after his trade to the New York Yankees.
Creditors will receive $75 million from the team in the bankruptcy plan, but the judge has said they can sue other entities of Hicks Sports Group, which defaulted on about $525 million in loans last year. Hicks is co-owner of the Liverpool football club, which is for sale, but the London sports team is not part of Hicks Sports Group and is safe from creditors in the Rangers' bankruptcy case.
Hicks will not be part of the new organization.