It is believed they successfully sold themselves to Hamilton on the basis that new chassis and engine regulations should favour them in 2014.
Jordan drew comparisons with another former world champion who went on to revitalise a big team's fortunes.
He said: "Michael Schumacher transformed Ferrari when he went there, and they were certainly lacklustre before he arrived. I think Hamilton will make a big, big effort at Mercedes."
The move ends an affiliation with the Woking-based outfit for Hamilton which stretches back to 1998 when he became the youngest ever driver to secure a Formula 1 deal aged 13.
Jordan continued: "It is a big shock for Formula 1 in the context that most people felt he was a lifer to McLaren. He was nurtured and brought on by Ron Dennis and the world at large felt that was where he would end his career.
"This will have been a very big decision for Lewis because of the family context. He has been in there since 13 and probably felt so comfortable.
"However, there were some things niggling away and some little demons in there getting into his head. There have been a number of little items unfolding that gave me the impression things were not quite as we thought or hoped at McLaren.
Hamilton got an early taste of fame after three appearances on BBC Children's programme Blue Peter
"His new management team probably were very much behind this because they want to make him into a global name just like they have done with David Beckham and the Spice Girls."
Mercedes have agreed a more financially lucrative contract with Hamilton than the one offered by McLaren, but BBC Radio 5 live commentator James Allen said it is wrong to believe the decision has been motivated by money.
He said: "He is not getting into a faster car at this point, but it would be wrong to say it is all about money.
"They will give him more money and more freedoms to make money outside his contract, but history in F1 tells you that you build a team around proper managers and engineers, then the last piece of the jigsaw is the driver.
"There have been signs Hamilton's relationship with McLaren was coming to an end, and if he had signed a new contract with McLaren it would have been like a couple staying together for the children."
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