The 26-year-old keeper, along with Birmingham midfielder Sebastian Larsson, completed a free transfer move to the Stadium of Light on Friday after signing a three-year deal.
Westwood, one of the most highly-rated goalkeepers outside the Premier League, joined after his Coventry contract expired and is hoping top-flight experience will help him push Given all the way for the number one spot in Giovanni Trapattoni's squad.
No Given: Keiren Westwood (No 1) wants a regular spot for Ireland
He told SAFC TV: 'Obviously, that is very difficult. Shay Given is an amazing goalkeeper and he has dominated the goalkeeping situation for Ireland for many years now.
'That's another challenge that I have been chipping away at for the last couple of years, and hopefully playing in the Premier League will make it a bit of a challenge for him.'
Westwood, who has seven senior caps to date, will go head-to-head with Belgium international Simon Mignolet for the number one spot at his new club at the start of next season with ?9million man Craig Gordon sidelined by a knee injury.
The Scotland international's future has been the subject of some speculation with his contract entering its final year, and the newcomer will hope to have made himself central to manager Steve Bruce's plans by the time he is ready to return.
Step up: Westwood will challenge Simon Mignolet and Craig Gordon at Sunderland
Bruce said: 'Keiren has proven to be an exceptional goalkeeper both in the Championship and at international level and he has certainly been one of the best in this country outside of the Premier League in recent seasons.
'We are obviously delighted that Keiren sees his future here at Sunderland, and we are looking forward to him joining what is a talented group of goalkeepers at the club.'
Larsson, of course, already has plenty of Premier League experience under his belt having been signed by Bruce for Birmingham from Arsenal in January 2007 following a successful loan spell.
The 26-year-old Sweden international admitted Bruce's presence on Wearside had been a major factor in his arrival.
Long term target: Steve Bruce managed Sebastian Larsson at Birmingham
He said: 'I have worked with the manager before and that obviously made the decision easier, but mainly it feels like it is a huge club and it feels like a great challenge for me.
'I want to take the next step in my career and I really feel I can do that coming to Sunderland.'
Bruce was delighted to have finally captured a man who has been in his sights for some time.
He said: 'Seb was a fantastic young player for me at Birmingham and he has matured into a very good midfielder.
'He has been courted by a number of top clubs over the summer - both in England and across Europe - so we are naturally delighted that he has chosen to come to Sunderland.'
The double signing brings Sunderland's close-season tally to date to six following the arrivals of Ahmed Elmohamady, Connor Wickham, Ji Dong-won and Craig Gardner.
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Explore more:People: Craig Gardner, Shay Given, Steve Bruce, Sebastian Larsson, Craig Gordon Places: Birmingham, Scotland, Republic of Ireland, United Kingdom, Ireland, Belgium, Europe