Harris, who played alongside the skilful trio of Peter Osgood, Charlie Cooke and Alan Hudson in the 1960s and 1970s, is also excited at the way the Premier League champions are starting to trust in youth again after years of big spending.
"Josh is one of the brightest prospects I've seen for quite some time," the 66-year-old former hard-man defender told Reuters in an interview.
"Provided he keeps his feet on the ground I think he's got a fantastic future with Chelsea," added Harris who played in a record 795 games for the club and now works as a match-day host at Stamford Bridge.
Most of McEachran's appearances have been as a substitute although manager Carlo Ancelotti showed his faith in the teenage midfielder by starting him in two Champions League games this season and in this month's 7-0 FA Cup win over Ipswich Town.
Patrick van Aanholt, 20, sent out on loan to Championship team Leicester City this week, and his fellow Dutch defender Jeffrey Bruma, 19, are other youngsters who have featured for Chelsea this season.
"Of the three lads who have come into the frame, Josh is top of the tree," said Harris who captained the club to FA Cup success in 1970 and European Cup Winners' Cup glory a year later. "He has done tremendously well.
"He is a very confident lad on the ball, seems to have two good feet and knows when to play the ball and when to hold it," added Harris of slightly-built, 5ft 10in England under-17 international McEachran.
"I've heard one or two people say he's an Alan Hudson-type of player. The games I've seen him in he has played in the holding role but some people tell me he is best going forward so it will be interesting to see him in that position.
"Van Aanholt has done ever so well in the games he's played and is a full-back who likes to get forward. Bruma looks a bit raw to me and I think it would do him good to go out on loan for a spell so he could play top-class football week-in week-out."
BRIGHT FUTURE
Harris said times had changed from the days when Chelsea were renowned for blooding inexperienced players.
"It's been a long time since we've had good youngsters coming through," he explained. "If you think back to the early 1970s when we won the FA Cup and Cup Winners' Cup we had six home-grown players.
"Managers don't seem to get much time now to bring young players through. It's been a long time since we've had players coming through the ranks but with these three young lads I think the future's looking very bright for Chelsea," added Harris.
"I had the pick of quite a few clubs when I left school but I picked Chelsea because they gave youngsters an opportunity. A lot of people say Chelsea just want to buy players so it's quite a feather in their cap if any young lads come through."
The slump in form suffered by the champions in November and December means they now trail Premier League leaders Manchester United by 10 points with 15 games to go.
Harris said Chelsea must go on a long run
