The Reds headed into the game facing the uphill task of overturning a 3-0 first leg deficit from their trip to Camp Nou last week.
Divock Origi put the home side ahead in the seventh minute when he finished from close range to set the tempo for the hosts.
The Reds went in 1-0 at the break, and substitute Georginio Wijnaldum made it 2-0 in the 54th minute, before the Dutchman added a second with a brilliant header just two minutes later.
The comeback was complete when Origi expertly guided home the fourth with 11 minutes to go after a quickly-taken corner by Trent Alexander Arnold.
Liverpool FC controlled the game and kept FC Barcelona at bay for most of the second leg clash as they booked their place in the Champions League final for the second season running thanks to their 4-3 aggregate win.
Celebrity Arsenal fan and former Daily Mirror editor Morgan was clearly extremely impressed by what he saw from the Reds on Tuesday night.
After the final whistle, Morgan wrote on Twitter: “INCREDIBLE!!!!! Congratulations Liverpool, greatest comeback in the history of football. 3-0 down to the best team in the world, and you destroyed them 4-0 in the 2nd Leg. Astonishing. And wonderful.”
Liverpool FC will take on either Tottenham Hotspur or Ajax in the Champions League final in Madrid on 1 June.
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