The 27-year-old Clarke has dedicated his 110 in the Australia first innings total of 479 for seven declared to the memory of Graham Bingle, father of his fiancee Laura Bingle, who lost his battle with cancer earlier this month.
The Australia vice-captain missed the opening Test of the three-Test series which the visitors won by 95 runs last Monday at Kingston after he had been granted compassionate leave to stay behind in Australia to support the Bingle family at a difficult time and attend the funeral.
"It was obviously a very emotional, a very special hundred for me because of what has happened over the past month or so for me back at home," Clarke said.
"All of my family and all of Laura's family wanted me to come over and play and be part of my first Test tour in the West Indies.
"It's hard being away from Laura and her family, but it's obviously very special, and it was very special to make a century knowing that my father-in-law to-be would have certainly been proud of me.
"He told me (before he passed away) to come over here and play. He didn't want me to stay at home, so it was special to make this hundred for him."
Clarke acknowledged a few tears rolled down his cheeks, after he drove Daren Powell for a straight boundary to reach his landmark.
"No doubt I wanted to make a hundred for (Graham), no doubt because I knew he wanted me to be over here playing cricket, he didn't want me back at home," Clarke said.
"I was so excited to score another Test hundred - my first one in the Caribbean, first one as vice-captain of Australia, and 470 runs on the board in our first innings - so there's obviously a lot of emotions there, but a big part of it personally was to do it for him."
Clarke took the attack to the West Indies bowlers, striking the ball cleanly, especially through the off side where he played several beautiful drives.
He raised his century with a lovely on drive off pacer Daren Powell, one of the 12 fours he struck during the innings which spanned 187 balls and 281 minutes.
Although he had not played cricket for almost two months, Clarke batted fluently from the time he arrived at the crease about 45 minutes before the scheduled close the previous evening, and hardly placed a foot wrong.
"I felt prepared, and I felt the work I did at home when the guys went and played in the Indian Premier League was a good idea," he said.
"A lot of batting was indoors and against bowling machines, but I did a lot of drill stuff, a lot of technical stuff and then once I've arrived in the Caribbean, I've done as much batting as possible in the nets, so I've have had a lot of support from all the coaching staff, net bowlers from the West Indies, and our own bowlers.
"I've did a lot of batting, but it was just game time that was going to be my issue. I guess, to me, my sole focus was to make sure I spent as much time out in the middle as possible to help set up the rest of this Test series and the One-day Internationals coming up as well."
Clarke followed up his superfluous batting with two late wickets that left West Indies in a bind, as they reached 125 for three when stumps were drawn on the second day.
"If the captain keeps throwing me the ball, I'll keep taking bowling seriously," he said. "I enjoy every opportunity I get to bowl, and hopefully I'll continue to play a part during this game."
Clarke collected the scalps of Xavier Marshall and Runako Morton in seven overs that cost seven runs.