In one message obtained by the Mail on Sunday, the Prime Minister thanked Mrs Brooks for letting him ride one of her horses, joking it was "fast, unpredictable and hard to control but fun".
In another the journalist, who faces trial in connection with the phone hacking scandal, praised Mr Cameron's speech to Tory conference, saying: "I cried twice."
The playful texts are apparently part of a cache of texts and emails handed to Lord Justice Leveson's media standards inquiry.
More top news
Scientists suggest that in 30 years antibiotic resistance will likely kill more people globally than cancer and diabetes combined.
Having a longer pregnancy also reduced the risk of suffering from post-natal depression, a study found.
A letter written a day before the Titanic sank by one of the disaster's victims has sold for a record-breaking £126,000 at auction.