The 16-year-old was linked to a move to Manchester City last month, but Liverpool pounced to salvage the failed attempt by their Premier League rivals which should provide relief to the struggling coffers of their neighbours.
The League Two side famously sold former England international and current Fulham captain Danny Murphy to the Reds 15 years ago, but though Murphy was an established Alex player at the time with 132 league appearances to his name, Smith has yet to appear for the senior squad.
The youngster announced the move on his Twitter page, posting a picture of himself alongside current Anfield boss Kenny Dalglish with the caption ‘signing for Liverpool’.
Crewe spokesman Rob Wilson said: “We are naturally disappointed that Dan has decided to sign for Liverpool.
“The club has received an undisclosed fee and future add-ons but we would have much preferred to have seen him play for our first team.”