Green played second fiddle to Julio Cesar in the Premier League last season but is now keeping the Brazil international out of the team.
"He had difficult circumstances when Julio came in and he had to sit on the bench for long periods," said Hill.
"It shows the character that he is. He has been outstanding this season. He has been a massive part of this roll we have been on at the moment."
Green's fifth consecutive clean sheet in Wednesday's 0-0 draw with Brighton sent Rangers top of the table, and he needs just two more shut-outs to equal a club record, starting at Yeovil this weekend.
But Hill added: "We don't want to jinx that! I am sure we will take a 2-1 win on Saturday."