Scottish Football: Rangers appoint former Newcastle United man as new CEO
The Scottish Championship club made the announcement to the Stock Exchange ahead of Monday's annual meeting.
Englishman Llambias, 58, a former managing director of Newcastle United, joined Rangers' board as a non-executive director in November.
The Scottish FA announced last week that it was investigating Newcastle owner Mike Ashley's role at Ibrox.
Rangers and Ashley have been accused of breaking several SFA rules relating to his stake in the club and have been called to a disciplinary hearing on 27 January.
Loans from the English businessman, whose Sports Direct company has control of Rangers' shirt sales and retail division, have kept the Glasgow club in business over recent months.
And Rangers told the Stock Exchange: "In line with the cost-cutting exercise announced on 12 November 2014, Mr Llambias's remuneration will be significantly lower than previously offered for this position."
Rangers and Ashley have already been called up in front of the Scottish FA to explain their position in terms of his dual role between Rangers and Newcastle. That will be heard in January.
But this leaves no-one in any doubt about where Rangers are heading - and who with.
Llambias' main priority now, as well as getting that much-needed cash into a club that at the moment has no money, is to face shareholders at a much-anticipated annual meeting on Monday. Shareholders are looking for answers and he will have to be the man now to provide those answers.