The Wales international is currently recovering from a thigh injury and hopes to soon be back in action to boost the Gunners' Barclays Premier League title bid and push to win the FA Cup.
The 23-year-old scored 13 goals this season before his latest fitness setback and following the announcement he had joined Santi Cazorla and promising teenager Gedion Zelalem in penning a new deal, Ramsey was relishing the challenges ahead under manager Arsene Wenger.
"I feel like there's plenty more to come. This season I've proven a lot of people wrong," Ramsey told Arsenal Player.
"There was a tough time in the period after my injury, but I've got through that and I feel really confident and feel like I'm improving with every game.
"Hopefully now I can get back out onto that pitch as quickly as possible and show what I'm capable of doing and hopefully finish off the season in some style as well."
Ramsey was signed from Cardiff when he was a raw talent in June 2008, and has recovered from the setback of a double-leg break at Stoke in February 2010 to become an integral part of Wenger's latest generation.
The midfielder added: "I am delighted to have signed a new contract. I have been here for six years and I am so happy.
"I think we have shown so far this season what we are all about and the direction that this club wants to go in.
"I want to be a part of that, and to be a part of something special at Arsenal. We have a great team which we believe can achieve great things."
Ramsey feels he can take his game to another level under Wenger.
He continued: "I have been a lot more composed in front of goal and taking my chances, been more consistent week-in, week-out so I would say this has been my best season so far.
"I think [to get to the next level] I need to go into the big games and to really show my authority on those games, to grab the game by the scruff of the neck and show everybody you can do it in the big games on a consistent basis. I think that will be the next step."
Cazorla, meanwhile, feels Arsenal stand on the verge of another chapter in the club's history, with Wenger poised to take his side to Wembley in the FA Cup semi-finals against Wigan, with either Hull or Sheffield United awaiting the winners.
The 29-year-old Spaniard, who joined from Malaga for £15million in August 2012, said: "I think that we can be a big player in competing for the top trophies in years to come and that's important for me.
"I have already had lots of good moments here and hopefully there will be many more to come.
"One of the main reasons for coming here was to get better as a player and joining Arsenal has definitely made me a better player."
Arsenal have also seen the likes of Tomas Rosicky and Per Mertesacker commit their futures to the club recently, although there has as yet been no confirmation on negotiations with defender Bacary Sagna, out of contract in the summer - or indeed Wenger's own situation with the offer of a new deal for next season as yet unsigned.
The Gunners boss said in reaction to Tuesday's announcement: "We are very pleased that Santi Cazorla, Aaron Ramsey and Gedion Zelalem have committed their futures to the club.
"Cazorla and Ramsey are absolutely key players for us, and this news is a boost to the whole club.
"Gedion is very young of course, but he has shown already that he has fantastic promise, and we all look forward to his development with us."
Wenger, meanwhile, will take charge of his 1,000th match when Arsenal travel to Premier League rivals Chelsea on Saturday.
Midfielder Rosicky, whose early goal secured the 1-0 win at White Hart Lane, feels that achievement is unlikely to be matched.
"It is absolutely unique - I don't think that anyone will repeat something like that again," the Czech international said.
"He is a legend for this club and I don't think anyone else will repeat it."