The administration of Boston Mayor Marty Walsh said it is reviewing an agreement the city struck with the Boston Red Sox in October that formalized a long-standing arrangement allowing the club to close off Van Ness Street during Fenway Park events.

The agreement, signed by Red Sox president Larry Lucchino and Mayor Thomas Menino’s police and transportation commissioners, makes permanent what appears to have been an informal arrangement between the club and the city allowing the team to close off the section of Van Ness next to Fenway during games. The Red Sox typically used part of the street for employee parking, paying no fee to the city to do so.

“We are currently reviewing the agreement, and compensation is one of the issues that we will consider during this review,” said Walsh spokeswoman Kate Norton.

The Van Ness arrangement dates back to 1945 when the Sox gave an easement to the city on land the club owned abutting Fenway Park. The easement, for which the city paid the club $1, allowed the city to construct Van Ness Street. The easement is recorded in the Suffolk County Registry of Deeds.

No mention is made in the easement of the Red Sox being allowed to close off Van Ness Street, but the arrangement has apparently been in place ever since. No other single private entity is allowed to close off a street in Boston on a regular basis.

The October agreement states that the closing off of Van Ness Street is, in part, a public safety measure. It is “necessary to enhance the safety and security of patrons to Fenway Park, nearby residents and business, and the citizenry of the city,” the agreement said.

The agreement also expands the Van Ness arrangement slightly, allowing the Sox to close off the street not just on game days but whenever an event hosting more than 2,500 people is held at the park.

David Friedman, the Red Sox special counsel and senior vice president, said signing the agreement made sense. “We believed it is appropriate for the city agencies charged with public safety and orderly transportation to confirm longstanding practices that have been in place for decades,” he said in a statement. “The formal confirmation enables Fenway Park to continue to operate safely and efficiently for baseball games and other large public events.”

Tom Tinlin, the city’s transportation commissioner under Menino, declined comment. The other signatory, Ed Davis, Menino’s police commissioner, could not be reached for comment.

The Van Ness agreement came four days before another deal that gave the Red Sox the rights, also in perpetuity, to close off the portion of Yawkey Way abutting the park during events to use as a food and entertainment court. That deal also maintains the storied Green Monster seats up in the air space over Lansdowne Street. In return for those rights, the Red Sox will pay the city $7.3 million over 10 years and then own them in perpetuity.

Gregory Sullivan, the former inspector general who is now director of research at the Pioneer Institute, a conservative think tank, said the city should have been compensated more for the Yawkey Way deal and paid something for the Van Ness arrangement.

When Sullivan was the inspector general, he urged city officials to seek compensation from the Red Sox for use of Van Ness Street.

“I can see that it fell on deaf ears,” he said. “The two deals were done as the curtain was coming down on the Menino administration so as to foreclose any possibility of the new administration undoing it.”