Norwich City Under-16s goalkeeper Remi Matthews signed a contract with City for him to become an academy scholar in the summer of 2010. He made his debut for the Under-18s during the early part of the 2009/10 season. He has great shot-stopping ability and has been with the Club since the age of ten.

Remi joined Wroxham on loan at the beginning of November 2012, making his debut in the 3-1 away win at Ilford in the Ryman League Division One North. He also spent time on loan at Leiston during 2012/13.

On 13th May 2014, Matthews signed a new two year professional contract with Norwich.

On 27th November 2014, Matthews was loaned to Burton Albion for a month following an injury to goalkeeper Chris Weale (on loan to Burton from Yeovil). He returned to Norwich without making a first team appearance for Burton but returned there on loan on 6th July 2015, signing until January 2016. He made his Burton debut against Scunthorpe on 8th August 2015, winning 2-1. He made a total of six appearances for the Brewers.

On 24th March 2016, he joined struggling League One side Doncaster Rovers on loan until the end of the 2015/16 season. He made his debut the following day against Colchester conceding four goals. He played nine times for Doncaster.

After signing a new two year contract with Norwich in July 2016, Remi was loaned to Scottish side Hamilton Academical for the 2016/17 season. He made 27 appearances.

After an impressive 2017 pre-season, Remi was playing for the Under-23s at the start of the 2017/18 season. However he signed for Plymouth on an emergency loan on 20th October 2017 becoming Argyle's fifth keeper of the season after Kyle Letheren hurt his thigh at Blackburn on Tuesday 17th October.Luke McCormick and Robbert te Loeke were also injured and youth team keeper Michael Cooper made his debut at Blackburn. Matthews made his debit at AFC Wimbledon keeping a clean sheet as Plymouth won 1-0. He made seven appearances in which he conceded six goals and kept four clean sheets before injuring his ankle against Portsmouth in late November. In December, Plymouth indicated that they were confident on re-signing Matthews on loan for the remainder of the 2017/18 season. He returned on loan to Plymouth on 29th December 2017 for the remainder of the 2017/18 season. He finished the season with 27 appearances for Argyle.

He was hoping to be City's first choice for the 2018/19 season but his form pre-season caused Daniel Farke concerns and he brought in Tim Krul as his number one. Matthews then joined Bolton on loan on 12th August 2018 until January 2019 with view to a permanent move in the January transfer window. He made his Bolton debut in the 2-1 defeat to Leeds in the League Cup on 14th August 2018.

He returned to Norwich in January 2019 when a transfer embargo stopped Bolton signing any players. When this was lifted (by Bolton paying back loans to the PFA), they signed Matthews on a permanent basis as well as extending Gary O'Neill's contract until the end of the season. On 19th April 2019, Bolton were relegated from the Championship following a 2-0 defeat to Aston Villa. It was their 14th defeat in 18 games.

Matthews played 38 games in the 2019/20 season but Bolton finished bottom of League One suffering a consecutive releation. They had had a points deduction at the start of the campaign for going into administration. On 26th June 2020 it was announced Matthews would be one of 14 senior players released at the end of his contract on 30th June 2020. Remi then trained with Ipswich according to reports on 22nd July 2020. On 15th August 2020 the Eastern Anglian Daily Times suggested that Ipswich would instead move for former Northampton keeper David Cornell thus allowing Sunderland to move for Matthews. Matthews would come in as a direct replacement for Jon McLaughlin who left at the end of his deal. McLaughlin opted against signing a new deal with Sunderland and made a move to Scotland to link up with Rangers instead of remaining at the Stadium of Light. This was confirmed on 21st August 2020 with Remi signing a one year contract..He played under Black Cats manager Phil Parkinson at Bolton 

Remi was one of seven players released by Sunderland on 26th May 2021. He had played a total of 10 games for Sunderland.

Matthews then signed for Crystal Palace on 13th July 2021 on a two year contract and will compete with Vicente Guaita and Jack Butland for a place in the first team. Palace's goalkeeping coach Dean Kiely was said to have played a key role in Matthews'decision to sign.

In the summer of 2022 he joined Scottish side St Johnstone on a season-long loan.

He finally made his Premier League debut when coming on as a late substitute in Crystal Palace’s 2-1 home defeat to title contenders Liverpool. Matthews was beaten by Harvey Elliott’s swinging stoppage time strike from the edge of the area at Selhurst Park, after an 87th minute introduction for injured first choice Sam Johnstone. “If someone came to me 20 years ago and said I would be playing in the Premier League I would have laughed and walked off,” he posted on his social media account. “Dreams really do come true. Proudest moment of my career for me and my family.“I’m 29-years-old now and it’s been a long nine years (since I first joined Norwich in the Championship), but I know how hard I’ve worked and I know how well I’ve done through the years. I’m happy to be here and make my debut, and now I’m going to look forward.