The Liverpool skipper has scored 94 goals in 428 Premier League appearances for Liverpool and won his 100th England cap in the 4-2 friendly defeat to Sweden in November.
He earned the FWA Tribute Award for making an outstanding contribution to the national game, with Hodgson and Rush keen to offer their praise.
"Since I have taken over the national team he has been outstanding, not only as captain but as a player," said Hodgson.
"For someone who has had such a good career, such a long career, to win 100 caps and play so many games for Liverpool, his only club where he was born and raised as a footballer, is a fantastic achievement.
"We see less and less of that type of player these days and I think Steven has all the attributes of a top-class footballer but also a top-class professional and a top-class person.
"It is an honour really to work with him."
Rush, who scored 229 goals in 469 appearances during two spells at Anfield, is equally enamoured with Gerrard's contribution to football.
He highlighted Gerrard's pivotal role in Liverpool's Champions League final victory over AC Milan in Istanbul in 2005, when, inspired by Gerrard, they came back from 3-0 down at half-time to draw 3-3 before claiming the trophy after a penalty shootout.
"It's been absolutely fantastic. It is a joy to watch someone like Steven play," said Rush.
"Going back to the Champions League Final in Istanbul, he was the main man that orchestrated that.
"He scored the first goal and gave everyone belief they could do that. He also scored important goals in FA Cup finals.
"People say who would get into the (Liverpool) team of the 80s that won everything and for me, scoring goals like that, Gerrard would walk into any Liverpool side of any era."