Arsenal met Partey’s £45million buy-out clause on transfer deadline day to bring the Ghanaian midfielder to north London.
The Gunners have been champions of England 13 times but have not won the title since 2003-04.
New Arsenal signing Partey said: ‘Everybody is wanting to win all the trophies that can be won. That’s my goal also.
‘It’s something that’s difficult but we’re working towards it and we’re ready. We have to go all out and try and achieve all I have said.
‘That’s the objective of the club and myself. We have to get back to where we belong.’
While Arsenal have not won the Premier League since 2004, they have won five FA Cups in recent years and beat London rivals Chelsea to win the competition last season.
They only finished eighth in the Premier League last term but already appear to have improved at the start of the 2020-21 campaign.
Under Mikel Arteta, Arsenal won the Community Shield in August and have taken nine points from a possible 12 from their four league matches to date.
‘It’s a great challenge,’ added Partey, who won the Europa League with Atletico.
‘They [manager Mikel Arteta and technical director Edu] told me about their plans and it was so exciting so I had to accept it. I feel great to be here.’
Following Partey’s move to Arsenal, Arteta said: ‘We have been watching Thomas for a while, so we’re now delighted to add such a high-quality player to our squad.
‘He is a dynamic midfielder with great energy. He brings a lot of experience from a top club that has competed at the highest level in La Liga and the Champions League for several years.
‘We’re very impressed with his attitude and his approach to the game. He’s an intelligent footballer.
‘We’re looking forward to him integrating into our system and contributing to the progress we’re building at the moment at the club.’