Dorrans, who won 12 Scotland caps during his career, signed for Albion from Livingston for £200,000 in 2008.
He went on to score 26 goals in 189 games for the Baggies - the majority of those in the top flight.
However, he will be most remembered by Albion fans for scoring 18 goals times during the 2009/2010 Championship promotion campaign.
Dorrans, 35, left Albion for Norwich City in 2015, before going on to play for Rangers, Dundee, Western Sydney Wanderers and most recently Dunfermline Athletic.
He left Athletic in September 2022 - but has now signed for the West of Scotland League Division One outfit.
Manager Jamie McKim said the signing was arguably the most significant in the club's history - but insisted the move is for football reasons.
He told Renfrewshire Live Sport: "We're absolutely buzzing to get this deal over the line.
"It's definitely the biggest signing we as a club have ever made. It's certainly one of the biggest ever signings at our level too.
"I first met him on a UEFA B licence course a few years ago, but I never imagined I'd be in a position to eventually sign him for Johnstone Burgh.
"For me it's really important people understand this was a football decision for both us and Graham.
"This isn't just about a name for us or for him to wind down his career. He's keen to come here because he wants to keep playing and keep winning.
"He's a winner. A Scotland international who has scored goals in the English Premier League and Scottish Premiership.
"I'm sure he's going to have a huge impact. His intensity and work ethic in training will rub off on the squad and I know he'll have a positive impact on our young players."