The contractor has called off a plan to appeal against a court ruling made last month that it must not shorten the brand to "McAlpine".
In a joint statement the two companies said they had resolved their differences. The statement said that Alfred McAlpine would amend its logo to include its first name.
The statement says: "Since the dispute commenced in October last year, both companies have continued to work together on the well known and highly successful Eden project in Cornwall."
In the ruling in the High Court, Mr Justice Mann said that the proposed rebranding by Alfred McAlpine amounted to an attempt to "pass itself off" as Sir Robert McAlpine.
He said that the name change had amounted to misrepresentation and would cause confusion among customers.
Sir Robert McAlpine had also claimed in court that the allegedly poor payment record of Alfred McApline might damage its reputation.
During the two-week hearing Ian Grice, chief executive of Alfred McAlpine, said that he had expected members of the McAlpine family would be upset by the decision to rebrand the firm. Sir Robert is still owned by the McAlpine family; Alfred is a publicly owned company.
Building disclosed in January that the case would hinge on an agreement made in the 1930s between two sons of the founder of the firm. The court heard that it was agreed that Alfred would operate in the North-west and Sir Robert in the South. The names were retained to distinguish the firms.
It is understood that the initial rebranding exercise by Alfred McAlpine to call the firm simply "McAlpine" cost £350,000. The High Court decision means that it will incur additional costs as the firm reverts to its original name.
It is also understood that Alfred McAlpine will have to pay the court costs of Sir Robert McAlpine as well as its own. It is believed that this could be more than £1m.