In one message, Cameron, the Conservative Party leader, thanks Brooks, 44, for letting him ride one of her family's horses, saying it was "fast, unpredictable and hard to control but fun", according to texts obtained by The Mail on Sunday.
In another, a gushing Brooks tells Cameron, 46, that she felt so emotional listening to his Tory conference speech in 2009 she "cried twice", adding: "Will love "working together".
Downing Street told BBC that the text messages were authentic and said the Prime Minister co-operated with Justice Leveson Inquiry, which is going into the culture, practices and ethics of the media here.
Much of the Leveson inquiry has taken up with questions about links between politicians and Rupert Murdoch's News International media company.
The two messages published by the Mail on Sunday were sent in October 2009, shortly after Brooks became chief executive of News International.
The existence of the messages has been at the centre of a row between Labour MP Chris Bryant and Cameron for several weeks and the contents will be a thorn in the prime minister's side, the British media commented.
Bryant has challenged Cameron to publish all the material himself, suggesting it was "too salacious and embarrassing".
A furious Cameron had rejected a demand in the House of Commons by Bryant two weeks ago to disclose all the texts and emails exchanged with Brooks, whose husband, the racehorse trainer Charlie Brooks, has been friends with Cameron since they both attended Eton.
Cameron and Brooks live near each other in Oxfordshire and Brooks went to Eton with the prime minister.
Brooks caused amusement at the Leveson Inquiry earlier this year when she revealed that Cameron signed some of his texts LOL, thinking it meant Lots Of Love, rather than Laugh Out Loud.
In her evidence to Lord Leveson, Brooks said Cameron sent her a text when she resigned in July 2011, telling her to "keep your head up".
She quit after the phone-hacking scandal led to the News of the World's closure, a paper she was editing when voice mails of murdered schoolgirl Milly Dowler's mobile phone were allegedly intercepted.
Lord Leveson is thought to be poring over a large amount of correspondence between Cameron, Brooks, and former Downing Street communications chief Andy Coulson, who formerly edited the News of the World, the BBC said.
Brooks and Coulson are awaiting trial accused of conspiracy to access voice mails. Brooks and her husband are also charged with conspiracy to pervert the course of justice.
