Greenberg, Simpson and Davis were all quizzed on Wednesday by the ownership committee, which approved the deal and sent it on for a further confirmation by Selig's executive council. The final step is a 75 percent vote of the owners or their representatives on Thursday.
"The Texas Rangers sale has been approved by the ownership committee and the executive council unanimously," Selig said late Wednesday afternoon. "There will be a big vote tomorrow. I'm delighted that we took the first two steps today in unanimity. Tomorrow we'll come out and tell you how the final vote came, but you can probably guess that."
Greenberg said that all the paperwork for the sale's closing -- contingent upon MLB approval -- has been signed and that the deal will be finalized as soon as that approval is granted on Thursday.
"There's nothing else that needs to be done," Greenberg said.
The Texas group was so excited and optimistic about the outcome after the two-hour ownership committee session was complete that Simpson and Davis immediately traveled back to Texas so they could attend Wednesday's Yankees-Rangers game in Arlington with star left-hander Cliff Lee on the mound. The Rangers entered the game in first place in the American League West, leading the Angels by eight games -- 10 in the loss column. Texas hasn't been to the playoffs since 1999.
"I don't want to be presumptuous and say it's going to be automatic," Davis said about the vote. "But we should be just fine tomorrow."
Greenberg stayed behind along with Kellie Fischer, the chief financial officer of the Rangers. Fischer will cast the change of ownership vote for the team on Thursday. Ryan remained in Texas and didn't take the trip.
"There was nothing we didn't expect at [Wednesday's] meeting," said Greenberg, a Pittsburgh sports attorney who already owns two Minor League teams. "It was a pleasure to answer their questions so they could get a feel for what our motivations and plans are and what the future will be."
The sale of the team became a necessity last year when Hicks defaulted on $525 million in loans involving his sports empire to a multitude of banks, and MLB asked Hicks to divest himself of the franchise. Hicks is reportedly also trying to sell his share of the NHL's Dallas Stars and Liverpool FC, a European soccer team.
Hicks originally settled on $575 million from Greenberg and Ryan, hoping the deal would be closed by Opening Day this year. But the creditors argued that the franchise would bring more money in an extended process.
Without agreement from the creditors, the Rangers were forced into bankruptcy in May, and last week's auction between Greenberg-Ryan and a group headed by Mark Cuban and Jim Crane followed.
Had Cuban, the owner of the NBA's Dallas Mavericks, and Crane, a Houston investor, prevailed, approval of the deal by MLB might not have occurred this quickly. The Greenberg group had already been vetted.
"I've always really believed in stability," Selig told reporters on Wednesday. "It's tough enough to run a franchise in stable times, and this was really difficult. Enormous credit must go to Nolan Ryan and Chuck Greenberg. It was a traumatic period. I guess, having run a franchise, I'm happy for Rangers fans, who have come out in great numbers this year.
"Last week was a very tough week. I know it was a difficult process. All's well that ends well. We're one step away from having a great ending, I think, for generations to come for the Texas Rangers."