After three seasons of the Britons working alongside one another at the Woking-based team, Hamilton has opted for pastures new with a move to Mercedes.
Although McLaren have long maintained a policy of equal status among their drivers, in many people's eyes Button is now de facto number one given he is 10 years older and more experienced than new team-mate Sergio Perez.
Formula One supremo Ecclestone certainly feels Button will step up to the plate as a leader for the team this season, although he is convinced Perez has what it takes to keep the 33-year-old on his toes.
Ecclestone said: "Maybe we will see their 'second driver' will not really be a second driver, that he is as good as everybody believes.
"I think it will be good for Jenson too, as he will now feel he is in charge, whereas before he might have thought he was 'number two'.
"Now he is 'number one' and we will very likely see a different Jenson. That might be good for him."
Ecclestone is also backing Mercedes to come good this year after a wretched return on their three seasons in the sport to date with just one victory during that time.
The 82-year-old certainly feels in acquiring Hamilton on a £15million-per-year contract, Mercedes sent out the right signals.
Speaking to the sport's official website, Ecclestone added: "First, in the tests they have shown they are much more competitive than in previous times.
"When I spoke with them about taking Lewis, I said if you take him you get the right sort of people because they think they are joining a winning team now.
"I am sure they will be competitive. I would be hugely surprised if they don't win races - on merit and not for other reasons."
To aid Hamilton's transition to his new team Ecclestone has even allowed the 28-year-old's new bulldog Roscoe a paddock pass.
Roscoe, who made his arrival on the F1 stage at the recent tests, is likely to be seen at a number of European races later this year.
Hamilton has every intention of taking him along, courtesy of the help afforded by Ecclestone.
Asked whether Hamilton had applied for a pass for Roscoe, Ecclestone said: "Yep, he has, and yes, he will get it.
"I am a huge fan of bulldogs. I have told him I would also be happy giving the dog a pass for the grid, and I will be happy to look after the dog while he is racing."
On a more serious note, Ecclestone is hopeful he will finally be able to float F1 on the stock exchange later this year.
Ecclestone had hoped for an initial public offering last year in Singapore, only to pull the plug given the instability in the market.
Ecclestone said: "Last year I thought the markets were not ready, but now it is getting more likely that there is an opportunity."
As to when a decision will be made, Ecclestone