The British vocalist was due to perform at the concert on Saturday, July 27 but cancelled her appearance due to "unexpected scheduling issues".
In a statement to her fans Rita Ora said: "This is something that myself and my team take very seriously as nothing makes me happier than performing for you.
“I’m so grateful to everyone that bought a ticket and I’m sorry that I can’t be there.
Fire destroys huge area of land at Great Denham Golf Course
Anglian Water rules out hosepipe ban for Bedford households
'Sophisticated crime group' behind £1.1m stolen from Luton council that was destined for a Bedford school
Man charged with burglary and assaulting an emergency worker in Flitwick
Bedford bus company revises timetable after passenger numbers review
“As always, I love you all and am beyond thankful for your support.
“I hope to return to Bedford soon and please go and support the night as Tom Odell and Tom Walker have stepped in and I know it’s going to be an amazing show."
Tom Odell and Tom Walker are now confirmed along with Fleur East and MistaJam for the new Saturday night line-up in Bedford Park.
Event promoter Mark Harrison said: “The show must go on, sadly without Rita, but the acts taking her place will make sure the night is one of Bedford’s biggest successes yet.
"The team worked around the clock to pull some of the most exciting talent in the UK for the line up.
"We are committed to bringing the biggest names in the music world to Bedford Park and my goodness I’m pleased and relieved to say we have delivered.
"Thank you to Tom Walker, Tom Odell and Louisa for stepping in at short notice. Come and join us for an amazing night in Bedford Park.”