"We have laid the foundations and now we want to win more. If we do that then we can be one of the most successful clubs for a long time to come and that is the aim," said Kompany after agreeing to the longest deal in the club's recent history.
The Belgian international defender was crucial to City's title run last year which culminated in their first top flight championship in 44 years.
"This Man City project was probably one of the most difficult projects in Europe to be part of and so far we have all done a good job even though a lot of people said it wasn't going to happen so quickly," he said.
"I like the kind of characters that we have in our team; I like the challenges we have ahead of us. Now is the time to build the culture of winning. We are in the right time; we are in the right moment," he said.
Kompany, who has won admirers for his calm and authoritative leadership as well as his intelligent defending said it never crossed his mind to consider a move.
"For me if you are good somewhere then there is no reason to look elsewhere," the 26-year-old said.
"Man City as a project is not just a project of the owners or the people employed by the club; it is also my project.
"I have been here since the beginning and I have seen everything at the club change inside and out. I have the feeling that I have contributed to it too. It is good to know that I can be at City for another six years. It is a compliment that the club feels so highly of me," he said.
The former Anderlecht and Hamburg defender, who has made 47 appearances for Belgium, said he particularly enjoyed the role of captain at City.
"I thrive on responsibility the more I get the more I perform; I am at the right club because I have built something here already.
"I have never denied that this can sometimes be the hardest team in the league of which to be captain; but like I said I am all about responsibility and challenge."
While excited to get started against next season, Kompany said he had savoured the close-season with fans on his travels, including the current tour of China, reminding him of the impact of the dramatic final day title triumph.
"That last game against QPR will be a very special part of City's history for the next 50 or 100 years but now is the time to look forward.
"I have travelled a lot this summer all over the world and our story has been a big story everywhere.
"It made a huge impact, including here in China and Asia in general. I met a lot of people in a lot of different countries and they have all got their reminders of the moment we won and how they experienced it in some way," he said.
"I can't wait to get started again. I am really excited about the season ahead."
