Neither firm would be drawn on the reasons why Cleveland Bridge has left the project.
Cleveland Bridge will be replaced by Dutch company Hollandia, a firm that worked on Swiss Re in the City.
The Cleveland Bridge statement said: "Cleveland Bridge regrets that this decision was communicated to trade unions yesterday by Multiplex, prior to the written confirmation of an agreement between the two companies."
The statement said Cleveland Bridge was informing its site staff about the situation.
A Multiplex statement said: "We can confirm that Hollandia is taking on responsibility for the on-site steel erection."
Multiplex said that it had reached agreements with Cleveland and Hollandia after "several weeks of discussions".
Multiplex added that a specialist management team from Hollandia had been on the Wembley site for several weeks and was now responsible for the steel-related erection.
The statement said that Hollandia's appointment would have no adverse impact on the construction timetable, which is still running well ahead of schedule.
It is understood that more than 200 Cleveland Bridge staff will leave the project and that many of the workers who could lose their jobs are considering picketing the site.