The incident, which took place shortly after 13:30 BST on Saturday, led to the evacuation and ongoing closure of the park.
An eyewitness described seeing Chapman wearing headphones and “pacing around” near the enclosure before he went in.
Mobile phone footage, believed to be from Chapman, appears to show the inside of the enclosure as he approaches the tiger across a patch of grass.
Chapman was a former pupil of the Jackie Palmer Stage School in High Wycombe.
“We loved watching William grow, both as a person and as a performer, during his time with us,” the school said in a tribute on Tuesday.
“It was a privilege to be part of his journey, and he will be remembered with great fondness by everyone who had the pleasure of knowing him.”
“Our thoughts and heartfelt condolences are with William’s family and friends during this incredibly difficult time,” the statement continued.
As a child, Chapman appeared in the ITV production May Contain Nuts alongside Shirley Henderson – who is best known for playing Moaning Myrtle in the Harry Potter films – and Darren Boyd.
He also portrayed Edward Jenner in the BBC series True Stories.
Staff at Yorkshire Wildlife Park have separately said their “thoughts and heartfelt sympathies” are with Chapman’s family and confirmed the rare Amur tiger, called Altai, remained in the enclosure and would not be euthanised.
Dan Swaine, the local authority’s executive director of place, said the council was “deeply saddened” by the incident and sent its “deepest sympathies” to Chapman’s family and those who were at the scene.