Egypt striker Salah, who had painful memories of last year's final defeat by Real Madrid after suffering a shoulder injury, got his side off to a flying start in Madrid by lashing home from the penalty spot after a handball from Moussa Sissoko.
Tottenham kept their heads after a nightmare opening and came to life when semi-final hat-trick hero Lucas Moura came off the bench but, with Harry Kane lacking sharpness after an ankle injury, another miraculous European comeback proved beyond them.
Liverpool did not produce much of their usual whirlwind attacking football but they were more intelligent and powerful than Spurs and sealed a sixth European Cup triumph with an arrowed finish from substitute Origi in the 87th minute.
The win was sweet redemption for Salah and especially German Klopp, who had suffered defeat on his last six appearances in major finals, including Champions League showpieces with Borussia Dortmund in 2013 and Liverpool last year.
His opposite number Mauricio Pochettino took a bold but ultimately misguided gamble in fielding Kane, who had only returned to full training a week ago after almost two months out with a serious ankle injury and struggled to influence play.
Kane was far from the only player who lacked sharpness in a game of few moments of real quality, a possible effect of both sides not playing any competitive games for three weeks.
Spurs put Liverpool under real pressure in the latter stages as Dele Alli headed over and Son Heung-min and Moura forced impressive saves from Brazilian goalkeeper Alisson Becker.
Origi, one of Liverpool’s heroes in their stunning semi-final second-leg turnaround against Barcelona, then killed the game with a ruthless finish into the bottom corner.
