The pair were confirmed as team-mates on Thursday with the experienced Button preferred to Danish rookie Kevin Magnussen alongside Alonso.
Spaniard Alonso returns for his second spell with the team, having spent the last four years with Ferrari, as McLaren look to improve on their fifth-place finish in the constructors' championship last season.
Dennis feels each driver has separate roles to play next term but expressed his confidence that the pair can complement one another.
"Fernando is coming back and he is going to prove that he is an absolute winner – that is the easy bit - and that he can reintegrate with our team and really work on fulfilling our common objective," Dennis told a news conference on Thursday.
"I really respect that Fernando chose to change direction, come back to McLaren and address what we both feel is unfinished business.
"For Jenson he has to play his own role. He has his own hurdles to jump, some of which have been quite deliberately put in front of him from the perspective of assisting with the decision.
"Of course I fully recognise [the decision] has been quite long in coming."
Magnussen reacted in bullish fashion to being dropped by McLaren - tweeting "No caption needed" alongside a picture of Arnold Schwarzenegger playing the lead character in blockbuster film The Terminator, seemingly suggesting he would 'be back'.
However Dennis - who confirmed Alonso's return was sealed some weeks ago - adding that he felt McLaren now had the best line-up in the sport.
"We signed Fernando a little while ago, but we decided not to announce the fact until we had also re-signed Jenson as his team-mate," Dennis added.
"For many reasons our negotiations with Jenson took quite a long time, but, now that they have been concluded we are confident that our collaboration with him will continue to thrive in the future every bit as well as it has in the past.
"Make no mistake about it, Jenson is 100 per cent committed to McLaren-Honda, to Formula 1, and to winning.
"As a pair, he and Fernando are supremely experienced. I can safely say, therefore, that we now have by an order of magnitude the best driver line-up of any current Formula 1 team."