The Swede left the club on Sunday after the Reds' relegation to League One was sealed with a 2-1 defeat at Huddersfield Town on Friday night.
Devaney will take charge of first team affairs, assisted by Tom Harban and Jo Laumann for Barnsley's final three games, starting tomorrow night against Blackpool.
The former Barnsley and Cheltenham Town player insists he is not focusing on what the future holds.
"I'm just concentrating on the here and now. It is a football club I love and had six great years here as a player," he said.
"I can confidently say I am a Barnsley boy now. I have done many roles in the academy and worked my way up. I am fully prepared for this opportunity.
"I have got the opportunity now and I am going to enjoy it. There is no pressure on me and I have relayed that to the players."
Current Wycombe Wanderers boss Gareth Ainsworth and Cheltenham manager Michael Duff are also contenders with the bookmakers, with both priced at 6/1.
Daniel Stendel, who guided Barnsley out of League One in the 2018-19 campaign, is 10/1 - the same price as Jonathan Woodgate, who played for Newcastle United, Leeds United and Real Madrid before moving into management.
Neil Warnock, who announced his retirement earlier this month but did admit he would have taken the Barnsley job this season, is 20/1.
Next Barnsley manager odds (correct as of 2.30pm, April 25, 2021):
Martin Devaney 2/1
Gareth Ainsworth 6/1
Michael Duff 6/1
Jonathan Woodgate 10/1
Daniel Stendel 10/1
Simon Grayson 12/1
Lee Johnson 12/1
Tony Pulis 14/1
Paul Warne 14/1
Mick McCarthy 14/1
Neil Lennon 16/1
David Unsworth 16/1
Jimmy Floyd Hasselbaink 20/1
Paul Tisdale 20/1
Neil Warnock 20/1