Ince had asked to have until Friday to consider Cardiff's offer after the two clubs agreed an £8m fee earlier in the week.
But the England U21 midfielder has opted to remain at Bloomfield Road - for the time being at least - where his father, Paul, is manager.
Cardiff confirmed Ince's decision, which they said was down to family reasons, on their website: "We can confirm that Blackpool midfielder Thomas Ince will not be joining the club.
"Having agreed a fee with Blackpool FC towards the end of June and with the
player and agent happy with personal terms offered, Blackpool manager and
Thomas' father Paul confirmed on Friday that, due to the recent birth of Thomas'
first child this week, the player didn't want to leave his family or the Seasiders at this stage of his life."
Speaking on Thursday, Cardiff manager Malky Mackay remained hopeful of landing the 21-year-old.
"I can only say from the chat we had, we had a very amicable, friendly chat and they asked me a lot of questions about where his career could go forward, where I see him in terms of the type of player he is and what's going on here," Mackay said.
"He was certainly very impressed by the stadium, training ground and the city in general during our conversation and the plans for Cardiff City going forward."