They signed by May 10, marking the end of an extension to their contracts.
Under the new agreement, the four unions will divide the Carpenters and Teamsters' work.
They are the International Alliance of Theatrical Stage Employees Local 8, the International Brotherhood of Electrical Workers Local 98, the Laborers International Union of North America Local 332, and Local 405 of the Iron Workers.
For this show, which was relatively simple to set up, 28 carpenters would have been hired Thursday for dismantling, a Carpenters' union spokesman said.
"We look forward to a very smooth move out tomorrow, and both our contractor and labor team are prepared," said Pete Peterson, a Convention Center spokesman. "We have a highly skilled, professional core workforce of union labor that has extensive experience and is more than capable of getting the job done."
Meanwhile, a leader of one of the four unions said Wednesday that his members would never handle any work belonging to the Carpenters and instead urged Convention Center management to bring the Teamsters and Carpenters back into the building.
"If the goal was to have all six unions sign the [Customer Satisfaction Agreement], then we have accomplished that goal and it's time to move forward and end this labor dispute now - before any irreversible harm is done," wrote Stephen M. Sweeney, general vice president of the Iron Workers District Council of Philadelphia.
Sweeney, a Democratic legislator who represents parts of Gloucester and Cumberland Counties and all of Salem County, is president of the New Jersey State Senate.
He oversees Local 405, based in Philadelphia. Its members, known as riggers, work in the center.
"I used to work in the center myself," he said. "We need harmony and peace in the Convention Center. This isn't creating peace."
Peterson responded: "Speaking from the perspective of the board of directors of the Pennsylvania Convention Center Authority and SMG, neither of those two entities have any desire to reopen the existing contract and risk undoing the partnership that we now have in place with the Laborers, Electricians, Stagehands or riggers."
SMG, of West Conshohocken, is the center's new facility manager.
On Monday morning, as a small group of Teamsters picketed the building, leaders of unions representing the Stagehands, Laborers, and Electricians led their members across the line to complete the final set-up for the BIO show, which opened in the afternoon.
The riggers did not cross the picket line. They weren't scheduled to work on Monday.
The riggers handle the heavy and complicated installation of exhibits. Compared with the five other unions that had worked at the Convention Center, the riggers have a relatively small workforce. It's unlikely they would have picked up much of the Carpenters' work anyway.
The Laborers and Stagehands would probably get most of the Carpenters' union work because their skills are closest to what carpenters do.
"We want to change the narrative from this idea that this is about the different unions," said Ryan N. Boyer, a leader of the Laborers. "The strong stand we took on this is because most of our members live in Philadelphia."
The new agreement is intended to make work at the Convention Center less complicated, particularly by allowing exhibitors more latitude in setting up their own booths.
Management and the unions believe the agreement will help business. They said management and labor conditions at the center had prompted some conventions, especially the largest, most lucrative ones, to go elsewhere.
Inquirer staff writer Joseph N. DiStefano contributed to this article.