Sean Decatur, president of the American Museum of Natural History, said Mr Griffin approved a long-term loan of Apex, as well as allowed scientists to take samples from the fossil for analysis.
"This partnership allows Apex to have pride of place at a museum world-renowned for its dinosaur collection and for its longstanding leadership in palaeontology," Mr Decatur said.
"It enables us to pursue specialised stegosaurus research centred around this extraordinary and scientifically important specimen."
Apex is the most complete specimen ever found, Mr Decatur added.
He said it was miraculous for a creature that had been dead for 150 million years to have about 80 per cent of its 320 bones preserved.
The specimen is also prized by scientists because it is estimated to have died at a relatively old age, and it could reveal insights into stegosaurus metabolism and bone growth.
Stegosaurus walked on four legs and lived in North America about 150 million years ago, during the Jurassic Period.
Scientists will make CT scans of the internal structures of the dinosaur's skull and analyse a small sample extracted from one of its giant thigh bones, a statement from the museum said.
"As exciting as is it is to have this dinosaur on display, it is even more exciting to have the opportunity to study it and make important scientific data available for research," Mr Benson said.
The museum's palaeontologists have a long record of breaking ground in dinosaur research, the statement said.
Commercial palaeontologist Jason Cooper discovered Apex on his land near Dinosaur, Colorado, on the Utah border near Dinosaur National Monument.