Zai Bennett, the channel's controller, told Broadcast that the three comedy series will not be returning with new episodes.
"[They were] good to the channel, but have had their time," he explained.
However, a Christmas special of How Not To Live Your Life is being planned.
Meanwhile, Bennett has ordered a review of programming including Snog Marry Avoid and The Lock Up but refused to say whether the shows would be axed.
"The whole point of a review is that we have identified there is an issue and we will work out what to do," he explained.
The news of the cancellations comes shortly after Bennett announced that he has ordered a new comedy series from Sharon Horgan and Holly Walsh and renewed Will Mellor's White Van Man.
Bennett also picked up two comedy pilots and revealed that BBC Three will air the US comedy Wilfred later this year.