The 48-year-old former Arsenal and England midfielder, whose success as Chelsea's assistant manager in the late 1990s was marred by a prison sentence for having unlawful sex with a 15-year-old girl, has had two previous management jobs, which were both unsuccessful.
The chairman of the Hearts' Supporters Trust, Martin Laidlaw, said fans would object to Rix both because of his criminal record and because he was "not the high-profile name we were promised". Laidlaw said: "The Hearts fans do not fancy him at all as we do not feel that he would be the right man for the job."
Rix's last management job, with Oxford, ended a year ago. He was in charge for 29 games, losing 15. Prior to that, he was the manager at Portsmouth between February 2001 and March 2002, losing half of his 56 games.
Hearts are set to confirm Rix's appointment, and clarify his precise role, at a press conference this afternoon. Club officials declined to provide information to the media yesterday, apparently because the club's majority shareholder, Vladimir Romanov, has taken exception to coverage of the recent events at Tynecastle.
George Burley left his job as manager after "irreconcilable differences" with Romanov, who then sacked his chief executive, Phil Anderton, and forced the resignation of his chairman, George Foulkes, who labelled him "a dictator".
Romanov is known to want a two-tier management structure, with a director of football working above the head coach, but there is no indication that a director of football is close to being appointed. Claudio Ranieri, Sir Bobby Robson and Ottmar Hitzfeld have already been rejected or declined the job.
"We made a decision [about Rix], we are happy," said Romanov's son, Roman, last night. Romanov Jnr is the new Hearts chairman and the club's acting chief executive. "We are very positive about it. We feel Graham has great energy and ambitions." Asked about the other post apparently available, he added: "We are not close to having a director of football."
Rix visited the Hearts training ground yesterday evening for a short, hastily convened meeting with the players. He addressed them as a group for two minutes, and then spent some time in discussion with the club captain, Steven Pressley.
Asked if he would be working under a director of football, he said: " Yes, but there is going to be a press conference and we will go into more detail then. I am delighted to have met the players and they are a good set of lads. I'm looking forward to working with them. I'm really looking forward to a big challenge. This is a massive chance for me and I am very grateful for the opportunity and I am determined to make a go of it."
1957: Born Doncaster, 23 October.
1974: Joins Arsenal as apprentice.
1976: League debut for Gunners.
1978: Wins first of seven England Under-21 caps against Finland.
1979: Gains FA Cup winner's medal as Arsenal beat Manchester United 3-2 in final.
1980: Misses last spot-kick in shoot-out as Arsenal's European Cup Winners' Cup final against Valencia goes to penalties.
1981: Makes England debut in 2-1 defeat by Norway in Oslo.
1984: Wins 17th and final England cap in 1-0 win over Northern Ireland.
1987: Joins Brentford on loan before moving to French side Caen and then to Le Havre.
1992: Moves back to Britain, playing 14 matches for Dundee.
1993: Chelsea manager Glenn Hoddle makes him youth-team coach.
1994: Makes last League appearance as a player.
1996: Takes charge of victorious England Under-21 team in prestigious Toulon tournament.
1998: Named Chelsea coach under player-manager Gianluca Vialli.
1999: Sentenced to 12 months in prison for unlawful sex with 15-year-old girl and indecent assault.
2001: Takes over as manager of Portsmouth.
2002: Sacked by Portsmouth with the team 15th in the table.
2004: Appointed as manager of Oxford United but moves "upstairs" after a poor run of results.
2005: March leaves the Us.
7 November appointed first-team coach at Hearts.