Vokes is now tied to the Turf Moor club until the end of the 2018-19 season.
"My massive goal is to do well at club level and play at the Euros in the summer," Vokes told BBC Radio Wales.
The 26-year-old, who has six goals in 37 games for his country, has been with the Clarets since joining from Wolves in July 2012.
He has scored 31 goals in 137 appearances in all competitions for Burnley, with a total of 64 in 300 career games.
He has netted five times in 27 games for Sean Dyche's side this season.
"It's great to put pen to paper, I've been very happy at Burnley, it's a club I've found a home at in the last few years," he said.
"We are concentrating on pushing for promotion and that was a massive factor in signing the new deal, the belief I have in the club.
"Promotion is a big aim and I think we've got the squad to do that."
A spot in Chris Coleman's 23-man squad for Wales' first major football tournament since 1958 this summer is another priority.
"I'm not guaranteed a spot, it's never a given or something I'd take for granted. You need to be playing well for your club to be picked for your country," Vokes added.
"I need to do well this season and that gives me the best chance of going to France and forcing my way into the team."
Vokes' 2014-15 campaign was hampered by a cruciate ligament injury but has suffered no problems since having surgery.
"Three-and-a-half more years shows faith from the club in me and they stood by me with my injury," he said.
"I'm over the injury, it's behind me now, but the club were great with me.
"Playing week in and week out has helped."
Striker Sam Vokes is aiming for promotion and a place in Wales' Euro 2016 team after signing a new contract with Burnley.