Cook was 102 not out when bad light ended play on the first day of the first Test of a four-match series. He'd been in for over four hours after England lost the toss in bowler-friendly conditions.
The 22-year-old opener, not included in England's World Cup squad, batted with the calm assurance that has been a hallmark of his brief international career, his century up in 162 balls with nine boundaries.
Essex left-hander's Cook latest Test hundred was his second at Lord's after he made 105 against Pakistan last year.
All-rounder Paul Collingwood was unbeaten on 21 after the weather meant only 56 of the day's scheduled 90 overs were bowled.
Fast bowler Daren Powell, who brought West Indies back into the game with two wickets after lunch, led the attack with two for 52 off 18 overs.
When a first bad light stoppage led to an early tea, England were 158 for two with Cook 82 not out and Kevin Pietersen unbeaten on 26.
The players were then presented to Britain's Queen Elizabeth II. Soon afterwards though the crowd voiced its impatience during the course of nearly an hour long interruption.
South Africa-born Pietersen appeared frustrated as well and, trying to hit his way out of a scoreless spell, he thrashed Corey Collymore's slower ball to cover where Devon Smith took his third catch of the innings.
Pietersen had failed to add to his score and England were 162 for three in the 45th over after a stand of 59.
After a second bad light stoppage, Cook went to 94 with a cut boundary off medium-pacer Dwayne Bravo, in what was the batsman's first Test against the West Indies, before a two off Powell saw him to three figures.
England, 85 without loss at the end of the morning session, saw stand-in skipper Andrew Strauss depart in the third over after lunch when he failed to get over the top of a square drive against Powell and was caught by Smith at point for 33.
New batsman Owais Shah, playing his first Test in England, made a nervy start that wasn't helped by being hit on the back of the helmet by a stray throw from Jerome Taylor.
But at the other end Cook, 47 not out at lunch, completed a 76-ball fifty.
Shah, on six, though was squared up by a fine Powell delivery that veered up the Lord's slope and was caught by third slip Smith, England 103 for two.
West Indies captain Ramnaresh Sarwan won the toss on a pitch freshened by several days of rain and in overcast skies.
But the new ball pair of Powell and Taylor rarely troubled the left-handed openers, the duo not helped by only West Indies' batsmen taking the field in their lone warm-up match, against Somerset, where two of the three days were washed out.
Strauss was leading England in the absence of injured first-choice skipper Michael Vaughan.
The Yorkshire batsman, who hasn't played a Test in 18 months because of knee and hamstring problems, was ruled out with a broken finger.
Also missing was Andrew Flintoff, the all-rounder suffering a recurrence of a left ankle problem.
This was England's first Test since their 5-0 Ashes defeat in Australia and first under new coach Peter Moores.
West Indies, who haven't won an overseas Test since 2000, also had a new coach in David Moore. They were playing their first international since the retirement of former captain Brian Lara, Test cricket's leading run-scorer, who quit after the World Cup.