The 35-year-old Dubliner prevailed in the playoff when Dredge had a bogey at No. 18 on the Adare Manor course. The last Irishman to capture the championship was John O'Leary in 1982.
'I have always said the Irish Open is like a fifth major for me, and to win it, well, I'm just ecstatic,' Harrington said.
Harrington started the day with a three-stroke lead and increased it to four with an eagle at the 631-yard, par-5 ninth, hitting a 3 wood within 8 feet of the pin. But he bogeyed twice on the back nine while Dredge had four birdies.
Dredge pulled even with a birdie at the par-4 17th. Harrington finished with a 71 and Dredge a 68 to leave both at 5-under 283, four strokes ahead of their closest pursuers.
'Bradley kept coming at me and I had to stay calm and collected,' said Harrington, Europe's No. 1 player last year. 'His birdie at 17 was a body blow.'
In the playoff, both drove into rough and put their second shots into more. However, Dredge's was on a downslope on a river bank.
While Harrington knocked his approach within 20 feet of the pin, Dredge's shot ended up on the far side of the river bank that cuts across in front of the green. Standing in mud, Dredge's fourth shot moved only about 6 feet, and when his chip-in attempt came up short, Harrington two-putted for victory.
'I'm a little disappointed at how it ended,' Dredge said. 'I thought I hit a good recovery at the last, but it ended in the hazard and I didn't have much of a shot.'
Simon Wakefield of England finished with a 72 for a 1-under 287 and third place, one stroke ahead of Richard Green (72), Louis Oosthuizen (72) and Andres Romero (71).