Jackson says he will look for other openings after his wedding next month. He said: "I will look to do more non-executive roles in the building, materials and support services sectors, and some company doctoring [when companies need financial help from banks]."
Babcock made an offer for Peterhouse in March, which was followed by the announcement of a possible counter bid by Jackson and Foster. This collapsed, but Jackson and Foster continued to advise shareholders to reject Babcock's proposals, even though the rest of the board recommended the offer.
Babcock said at first that it would take over the company only if 90% of shareholders accepted its bid, but last week it revised this figure to 50%. Jackson described the decision as "desperate".
Babcock's advisers made two complaints to the takeover panel that Jackson was privately influencing shareholders, allegations that Jackson denied.
Under stock exchange rules, Babcock had until Monday to declare the deal unconditional. Many doubted that Babcock would obtain the 50% approval required but it obtained 51.36%.
As the offer is now unconditional, Babcock can wait for further shareholder acceptances. Babcock needs 75% backing to pass special resolutions, such as changing the company's name.
Alan Robertson, chief executive of Peterhouse, confirmed the changes would include altering the firm's name, although infrastructure division Eve and rail subsidiary First Engineering will retain their brands.
Babcock chairman Gordon Campbell said that the enlarged group would now be better placed to bid for the complex projects coming up in the support services sector.
Peterhouse and Babcock have been accused in the past of relying on too few clients.