"It's time we got something back to put this thing to rest," McHale said Friday.
His unpaid leave is through July 31; Taylor's suspension ends a month later.
The league gave back the Timberwolves' 2003 first-round pick.
"We are pleased to put this episode behind us, so that we and the Timberwolves may focus our full energies on basketball rather than protracted legal proceedings," NBA commissioner David Stern said.
An arbitrator's hearing had been scheduled for Tuesday and Wednesday.
McHale, who handles general manager duties, said he didn't know about the deal between Smith and Taylor to circumvent the salary cap, and merely initialed contracts without reading them. He said he agreed to the leave of absence so the team could move on.
McHale and Taylor can't attend Minnesota games or practices, be present in the team's offices, or be involved in personnel decisions, the league said. Team lawyer Jack Regan was barred from representing the team through Aug. 31.
In October, Stern stripped the Timberwolves of five first-round draft picks and fined the team $3.5 million for the team's 1999 deal with Smith. It involved a series of secret contracts worth $86 million over seven years.
Taylor, who admitted the illegal contracts earlier and said McHale was unaware, announced this week he would accept a suspension.
McHale joked Friday about his enforced leave but also said he was embarrassed. When he found out he had initialed illegal contracts, McHale said, "I had the eerie sense that this was heading down a dark road." He said he considered going to arbitration but agreed to the leave of absence "hoping the whole thing would go away."
McHale also said NBA teams routinely try to maneuver around salary cap rules, and that league officials told him they needed to "send a message" through harsh sanctions on the Timberwolves.
"There are eight to 10 teams that do this all the time," he said. "They're just good at it. We're bad."
Of his lack of oversight, he remarked: "I haven't read a contract in four or five years. After reading the first one (years ago), I realized why I was a communications major."
Taylor has said coach and general manager Flip Saunders, director of player personnel Rob Babcock and assistant coach Jerry Sichting will share McHale's duties.
Smith signed a one-year deal with the Detroit Pistons last month for $2.25 million.
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