Murphy made 22 appearances for Albion last season, scoring six tries, as the club won 22 out of their 30 matches.
The experienced centre, a former St Boniface School pupil, wanted to stay at Brickfields, however, he was not able to agree a new deal with the National One club at the current time.
Cornwall star Murphy insists he understands Albion’s position, but said he needed to sort out his future.
“I would have liked to stayed on,” admitted Murphy, who said he was more than willing to take a pay cut.
“I thought we had built something and were going places.
“But I am really excited about this new challenge with Barnstaple.
“I know their coach (Steve Perry) very well. I learned some things from him when I was at Launceston. I am excited about the challenge.
“Barnstaple is a great club and the support they get is fantastic.
“National Two is a step up for them but it is something to look forward to.
“My future has been up in the air for so long now that it is nice that Barnstaple want me.”
Murphy started all four of Cornwall’s games as they retained the County Championship title last month.
Murphy’s departure comes on the day Albion announced former rugby league player Martin Hall as their new director of rugby and Dan Parkes as their new head coach.
Parkes is a former Albion player who made 53 appearances for the club between 2001 and 2005.
He returns to Plymouth from Brixham where he had been coach for seven years.
The ex-Royal Navy player said: “It is an honour to be asked to be head coach of Albion, a club I was proud to play for over a number of seasons.”
Former Wigan Warriors forward Hall was Parkes’ assistant for a short spell at Brixham. He was previously head coach at Halifax RFLC.
Albion will return to pre-season training on July 4.