Uncertainty had surrounded Coleman's future in recent weeks, with the 43-year-old linked to the vacant managerial position at Crystal Palace, but his new deal was confirmed at a press conference on Friday.
And Bale, who makes his return to the national set-up against Finland on Saturday after missing out on matches against Macedonia and Belgium through injury, is hopeful Coleman can lead the side to a major tournament for the first time since 1958.
"We've had a year with him now to get used to things, and hopefully now we have a bit of stability and continuity in the training and games," the Real Madrid attacker told the Football Association of Wales' YouTube channel.
"Everybody knows what they're doing and there's not new ideas coming in all the time, so it's something we're all looking forward to.
"We realise we have a chance (to qualify for a major finals) - I think more teams can qualify for Euro 2016.
"There's even more chance now that we can qualify and we see that as a big goal and something we want to take advantage of.
"It's always an honour to play for my country and something I look forward to do every time I pull on the shirt."
