The 25-year-old midfielder penned a two-year deal at Reading after turning down a new contract at Montgomery Waters Meadow, where he spent two seasons.
Laurent, who admitted to be 'sad' for leaving Shrewsbury, left a message of goodbye to on his social media, which was shared by the club, after his switch to The Madejski Stadium was confirmed on Tuesday night.
The former QPR and Wigan man enjoyed some memorable moments in blue and amber, most notably in FA Cup clashes, where he scored away at Stoke and Wolves and shone against a strong Liverpool side at the Meadow.
Laurent wrote: 'Although Reading is the move that I really wanted, it is sad to leave behind a place where I feel comfortable, happy and surrounded by a group of people who supported and helped me so much.
'I would like to thank the people of Shrewsbury and of course their amazing football club that have trusted and guided me.
'I loved my time at Shrewsbury, made some great friends and learned lots from some really good people. From the chairman, Brian Caldwell, John Askey and Adam Henshall who initially brought me to the club, Danny Coyne and Eric Ramsay who helped me along the way, thank you so much.
'To gaffer, Dean (Whitehead), and all the coaching staff, who brought me on further and allowed me to express myself (most of the time), thank you I am eternally grateful. My team-mates, thank you for always being there for me.
'To the fans of STFC it has been an honour and pleasure to wear the blue and amber shirt, thank you for the wonderful support, some great memories and your best wishes.
'STFC deserves the very best, it is a fantastic football club. I owe you loads. All my best wishes for the future. Josh.'
The midfielder, who was a target for Championship clubs in January, said in his first interview for Reading that Town will always have a place in his heart.
Laurent scored eight goals in 93 games in total for Salop.