Pools are on the verge of dropping out of the Football League for the first time since 1921 as they sit two points off safety with two Sky Bet League Two games to play.
Jones was appointed as Craig Hignett's successor in January but failed to turn the club's ailing fortunes around, picking up just 13 points from 17 games.
Experienced defender Bates will now attempt to preserve the club's League status and he will be assisted by captain Billy Paynter, Stuart Parnaby and Ian Gallagher.
A club statement read: "Hartlepool United can confirm that Dave Jones has left his position as first team manager by mutual consent.
"Assistant managers Alex Armstrong and Kevin Cooper have also departed The Northern Gas and Power Stadium with immediate effect.
"The club would like to place on record its thanks to Jones, Armstrong and Cooper for their efforts and wish them every success in the future."
Bates has been installed as Sky Bet's 4/1 favourite to take the job on a permanent basis.
Saturday's 2-0 loss to Barnet was the final straw and led to club president Jeff Stelling resigning after an extraordinary rant on Sky Sports' Soccer Saturday.
The presenter, known for his outward support of Pools, said on air: "We have lost at home, we're in the relegation places, and it's not personal Dave, but for God's sake for the good of the club walk now.
"Go now. You've got 13 points from 51, this is not your level of football.
"(Finance director) Pam Duxbury, the chairman Gary Coxall, if he won't walk, then sack him.
"If it means me resigning as president then I do so happily - do it now, do it today."
Jones felt Stelling's outburst showed "a lack of respect" and told reporters after Saturday's defeat: "It's okay Jeff Stelling saying it in his comfy chair. He doesn't know.
"In fact it's a lack of respect for me. Why should he say that?
"He's such a big hero, but I'll go up against him.
"Does he say it about anyone else? (Arsene) Wenger? It's not his job, his job is to report.
"He hasn't phoned me - a few weeks ago he's sat in my office crowing about us going five games without losing, how we've changed it around.
"What's changed? I haven't changed or has he forgotten that?
"I'm fighting for my life, how about a bit of support Jeff, rather than the rubbish you are giving out?"
Pools could be relegated to the National League on Saturday if they lose away at fellow strugglers Cheltenham and Newport win at Carlisle.
They finish the campaign at home to champions-elect Doncaster on May 6.
