The 30-year-old spent the majority of his career at Austria Vienna before moving to Germany and has signed a three-year contract with Brighton for an undisclosed fee.
Brighton manager Chris Hughton — in Austria preparing the team for their Premier League campaign — said Suttner had been a player he had fancied for a while.
“Markus is someone we have been aware of for some time, and I am pleased we have managed to complete the transfer at this stage, and he is now able to join us for the second half of the week,” Hughton told the club website.
“He has a great level of experience internationally, and in the top divisions in both his native Austria and Germany, where he has played the last two seasons with Ingolstadt, and that experience will serve us well.
“He will add competition at the back on the left side of defence, and I’m now looking forward to working with him.”
Suttner played in both the Champions League and Europa League for Austria Vienna before joining Ingolstadt when they were promoted to the Bundesliga in 2015.
He scored four times in 31 appearances for the German club last term which ended with them being relegated.