Filip, who has made five first-team appearances and can play left-back or midfield, has committed his future until 2015.
Midfielder Patrik, who was a regular goalscorer for the Celtic Under-19s in recent seasons, has signed a one-year extension, tying him to the club until the end of next season.
The 19-year-olds first arrived at Celtic Park in 2009.
Filip, who is awaiting the results of a scan on a groin injury, told the Celtic website: “We have learnt a lot since we have been here. The physical side changed a lot, but we are still the same players we have always been, our bodies have just progressed.
“I want to stay in the first team and hopefully win some more medals this year. Every trophy means everything and we want to win as many as we can in our careers.
Patrik has set his sights on following his brother into the first team.
“I have always dreamt about being the best player in every age group so I want to get there,” he said. “Filip is closer to it than me but I will get there.
“We’ve had so many years here so we didn’t want to leave. We wanted to stay because we’ve enjoyed it here. Our agent had conversations with the club and when the contract was finished we were pleased to sign it.”
Meanwhile, Celtic manager Neil Lennon insists his team are “a million miles away” from considering the prospect of a domestic treble this season.
With a weakened Rangers side relaunched in the Irn-Bru Third Division, Celtic are odds-on to retain their Clydesdale Bank Premier League title – although their start to the SPL season has been ropey and they currently lie third in the table.
The Parkhead club are also favourites to win the Scottish Cup and the Scottish Communities League Cup, in which they last night hosted First Division Raith Rovers in the third round.
Lennon was pleased with the convincing 2-0 home SPL win over Dundee at the weekend but was not for discussing success in all three domestic competitions this term.
“We are a million miles away from talking about that (a treble) at the minute, honestly,” said the Northern Irishman ahead of last night’s visit of Rovers.
“There is such a long way to go in the season. What I don’t want is for us to take our eye off the ball in any of the competitions. The approach has to be right, as it was on Saturday.
“It took us a while to break Dundee down and what we have to be mindful of is not getting sloppy and being complacent.”