The 37-year-old centre-back joined Rangers on a free transfer last week as manager Mark Warburton added much-needed steel to his rearguard ahead of their big return to the Scottish Premiership next season
Barton also joined the Ibrox club on a free transfer after the 33-year-old midfielder helped Burnley win Premier League promotion last season.
The one-time England international is a former team-mate of Hill's at, but Barton, who has also played for Manchester City and Newcastle United, says Rangers is the biggest club he's been at and warns the veteran that he'll need to adjust to the expectation.
"I spoke to Clint the other day and said to him ‘you won’t understand the size of the club’ and told him how big it is and that it’s probably the biggest I’ve played for so I think he’s in for a culture shock", he told Rangers' official site, via Inside Futbol.
Hill is the fifth new face to arrive at Rangers this summer, following in the footsteps of Barton, Jordan Rossiter, Matt Crooks and Josh Windass - the latter two signing pre-contract agreements in January.
But another of Hill and Barton's old colleagues from their West London days could be signing this week as The Mail reported that Niko Kranjcar is also joining.