Mercedes confirmed on Friday morning that Hamilton would be joining them on a three-year deal from the start of the 2013 Formula One season, ending a 14-year association with McLaren.
Hamilton will replace Michael Schumacher at the German team, with Mexican driver Sergio Perez - currently with Sauber - stepping in for the Briton at McLaren.
Hamilton has described his move as a "fresh challenge" but Whitmarsh believes the switch makes it less likely he will achieve his ambition of matching his hero Ayrton Senna and becoming a three-time world champion.
"Mercedes is a great partner of ours and they are a great team," Whitmarsh said.
"But for anyone leaving McLaren, and he wants to win, I think that's a mistake because I have faith and belief in this team.
"Whether you measure it over the last four races, four years or 40 years, we're a fantastic team.
"So I would say to any driver who wanted to win in this sport 'come and join McLaren and aspire to join McLaren'.
"I wouldn't advise anyone to leave McLaren if they want to win, but I've got to respect Lewis' decision and really wish him well."
Mercedes have won just one of 52 grands prix since taking over 2009 champions Brawn GP, while McLaren have won 16 over the same three-year period.
Whitmarsh, who was only informed of Hamilton's definitive decision two days ago, is adamant McLaren did everything in their power to keep hold of the 2008 world champion.
Whitmarsh added: "I know we made a very big financial offer, bigger than I believe any Formula One driver is enjoying today, other than himself.
"That is something that I am comfortable with. But ultimately we move forward now."
It is understood McLaren's initial offer was a pay cut of a third on his current salary, and only when Mercedes entered the negotiations did McLaren start to fight to hang on to their star name.
In the end, despite McLaren's recent form with four consecutive pole positions and three successive wins prior to Hamilton's retirement in Singapore on Sunday, the decision was the hardest of the Briton's career.
"We were working towards him staying, but we realistically knew there was always a chance he wouldn't," said Whitmarsh.
"He rang me two days ago, from Asia, and I believe I was the first person he told. We had a long conversation, a warm conversation.
"He rang me again yesterday and we had another long conversation. In the end, for all parties, you need to make a decision and move on.
"So we had to look at other options."
Hamilton has to believe Mercedes, with the talent of their backroom staff built up over the past few years by team principal Ross Brawn, will come good.
Aside from a reported £15million-per-year salary and greater freedom with regard to image rights and sponsorship appearances, Hamilton is a man who loves winning, and will not accept being second best.
Brawn will believe he has the missing piece to his puzzle to ensure Mercedes finally realise their potential and become champions.
Hamilton said: "It is now time for me to take on a fresh challenge and I am very excited to begin a new chapter racing for Mercedes.
"Mercedes-Benz has such an incredible heritage in motorsport, along with a passion for winning which I share.
"Together, we can grow and rise to this new challenge. I believe that I can help steer the Silver Arrows to the top and achieve our joint ambitions of winning the world championships."
In appointing Perez as Hamilton's replacement on a multi-year contract, Whitmarsh believes they have an "undeveloped" driver, but one with enormous potential as they partner youth with experience alongside Jenson Button.
Perez, a product of Ferrari's young driver academy, had been linked with a move to Maranello earlier this year as replacement for Felipe Massa.
However, Ferrari president Luca Di Montezemolo scotched that move by claiming Perez lacked the necessary experience, despite finishing on the podium on three occasions this season, most recently in Italy behind Hamilton.
Whitmarsh claims Perez has produced "a string of giant-killing performances", and now the 22-year-old is out to prove Di Montezemolo wrong.
Perez said: "The McLaren name is one of the greatest in the history of Formula One.
"For more than 40 years McLaren has been a team every racing driver has aspired to drive for.
"I'm under no illusion I've made a very big step - as it would be for any driver - but I'm ready for it."
As for Schumacher, the 43-year-old seven-times champion appears on the brink of retirement for a second time after a tough three years with Mercedes, epitomised by Sunday's crash in Singapore.
A move to Sauber to replace Perez has been mooted, but for now he said: "I have had three nice years with the team which unfortunately did not go as well as we all would have wanted on the sporting side.
"I wish Lewis well and for the team to achieve the success we worked so hard for in the build-up."