Financial terms of the transaction have not been disclosed. A closing date is also not known, as the deal is still subject to the approval of relevant authorities.
Until that time, Mammoet said, it and ALE will continue to operate independently.
Mammoet CEO Paul van Gelder noted that the companies complemented each other in terms of geographical presence on all continents.
"Together, we have a well-balanced portfolio of activities worldwide; this enables us to improve our service proposition and create synergies, as we are able to mobilise equipment and personnel swiftly anywhere," he said.
ALE managing director Mark Harries, who concurred, said the companies shared an ambition to be leaders in the sector.
"Both companies have a strong track record and are renowned for their craftsmanship, innovations and fleet of equipment. We both have shaped the profession of heavy lifting and transport through numerous innovations in the past decades."