Carroll, a bright-eyed, ungelded colt with explosive leg strength, was hurt while stretching to reach Steven Davis's sugar lump against Southampton.
Hopes that he could gallop it off quickly faded and, following the advice of doctors, West Ham have approached a Walthamstow adhesives factory with a view to sealing a permanent move.
Hammers manager Sam Allardyce said: "He's done his fetlock good and proper, so I'm afraid it's goodnight Gateshead. Time for Andy to go to the big nightclub in the sky. Never again will we see him galloping free through the grass, his nostrils flaring and his mane flowing in the wind.
"Saying goodbye was very emotional, because obviously Andy can't comprehend what's going on. But it's not right that he should suffer any longer. And nor should the fans who pay to watch him."
West Ham captain Kevin Nolan, nicknamed 'the Geordie Whisperer' for his uncanny ability to understand Carroll, said: "I've got great memories of riding around on Andy's back, controlling him by the ears and feeding him carrots when he did tricks.
"We always knew it might end this way, but I let myself hope he'd be another Ruud van Nistelrooy, going out to pasture on his own terms before setting up a hugely successful stud farm.
"He was a great team-mate and good friend. I'm sure he'll make a highly effective old-fashioned glue."
West Ham have confirmed that a portion of the glue will be reinvested in Winston Reid's hamstrings and on Carlton Cole's boots.
