The 22-year-old former Republic of Ireland Under 19 international left the Us' pre-season tour in Spain over the weekend to undergo a medical and complete the move, signing a four-year contract, for an undisclosed fee believed to be in the region of £1.6m-£2m.
McNally joins Scott Twine of MK Dons as Kompany's first signings for the club, with the centre back bolstering an area which has lost captain Ben Mee and England international James Tarkowski - with much interest in McNally's compatriot Nathan Collins.
County Meath born, McNally started his career at League of Ireland Premier Division club St Patrick's Athletic, and also spent a season on loan at Drogheda United in 2019, before joining Oxford in January 2021.
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He first made the first-team squad in April that year at Sunderland, and made his competitive debut in August in an EFL Cup tie at Burton Albion, with his league debut coming three days later at home to Charlton Athletic.
He has made 33 appearances for Oxford, scoring four goals.
Still a bit raw, McNally has vast potential, with many onlookers believing he is capable of playing in the Premier League in time.
McNally said: “It’s unreal to be here, I’m absolutely buzzing and so glad to have got the move done.
“It’s all happened so quick really, I just can’t wait to start now and I’m really excited.”
Kompany added: “Luke is a young player, he’s good on the ball, wins his challenges, and knows how to defend. We are delighted he is now a part of our squad.
“We are pleased to welcome him to our Club, he has shown all the qualities we were looking for in a central defender, and we are looking forward to working with Luke.”