The Scottish loose-forward ran out of time to prove his fitness after missing Saturday's defeat to the New Zealand Maori, and he will now officially be replaced in the squad by Welshman Ryan Jones.
"It has been a long time now and there is still a slight problem there. He is not going to be able to challenge for a Test place," said head coach Sir Clive Woodward.
The news is heartbreaking for Taylor, 25, who is a double Lion but has never started a game in the famous red jersey.
In 2001 he played as a second-half replacement in the tour opener against Western Australia, scored one try and created another brilliantly for Iain Balshaw before knee ligament damage prematurely ended his tour.
Taylor's injury jinx struck again last year when he suffered another knee problem and spent most of the year battling through flu, mumps, shoulder and ankle injuries.
Woodward rates Taylor so highly that he still won a place in the original Lions touring squad and it appeared his luck might have changed.
But that lasted just a matter of days. The hamstring injury which ruled him out of the opening game against Argentina on May 25 has finally cost him the tour.
Lions officials initially placed Taylor's recovery at 10-12 days. Three weeks later he was back in the match squad and preparing to start against the Maori when he felt "further discomfort" in his hamstring on the eve of the game and was forced to withdraw.
Officially it was for "precautionary reasons" but Woodward immediately feared the worst and sent for Jones, the Wales international loose forward, who arrived on Sunday and becomes the 49th Lion selected for this tour.
Taylor's fate was confirmed on Sunday when the Lions medical staff stated they could not guarantee that Taylor would be fit in time to available for the first Test.
Taylor said: "Obviously I am massively disappointed that my tour has ended this way - it is just an unfortunate coincidence that this is my second tour to end like this.
"I thought that I had a lot to offer this time round, especially having fought so hard to come back from injury over the past season.
"It is frustrating as I had been involved this week in full training sessions and my rehab had gone well but you have to be philosophical about these things, move on, concentrate on getting right.
"It is not a long term injury but with only a few weeks left of the Lions tour there are just no guarantees that it would be right in time.
"I still think that this group of players, despite Saturday's result, have the opportunity to be successful in the Test series - and good luck to Ryan.
"In the meantime I just have to focus on getting back for the start of the season over the next few weeks."
Woodward added: "Simon is hugely disappointed. There is not a lot you can say to him. It has been tough.
"Simon is a class player, and I feel for him but he has the character to come back from this and we wish him well in his recovery."
The Lions have now lost four players through injury - Taylor, Iain Balshaw (thigh), Malcolm O'Kelly (groin) and Lawrence Dallaglio (fractured ankle).
Taylor will now begin another two-week rehab programme in a bid to shake off the frustrating injury that has cost him so dear.