Morrison, 22, who is out injured with a knee injury until the New Year, is already the club captain while Obita, 20, has broken into the first team this season.
"It's wicked," Morrison told the club website. "We've been talking about it now since the end of last season and it feels great to finally get it done. Now I can concentrate on getting fit and getting back in the team.
"Captaining the side this year has probably been my greatest achievement in football and I want to be back out there as soon as possible."
Obita, who last month scored the winner against fellow playoff hopefuls Nottingham Forest, was delighted to continue his spell with his boyhood club.
"It's a club I've been at since I was eight years old, going through the ranks and now playing in the first team.
"So much has changed since I signed my first professional deal here, so to sign again is a fantastic feeling."
Reading are currently sixth in the Championship after 19 games following their relegation from the Premier League last season.