The 34-year-old, who won 65 caps for Scotland, has returned to the club fold ahead of this weekend's clash with reigning RaboDirect PRO12 champions Ospreys.
The Gunners are currently on a poor run of form that has seen them lose their last five league games and Jacobsen has vowed to help turn that slump around.
"Over the last few months the idea (of international retirement) has been going round on in my head," he said.
"And then being in camp for the All Blacks game I realised it was time. My commitment to it and my hunger is not what it was when I was a younger man and that made me realise it was time.
"I did not want to drag it out and play another couple of years dragging it out, the fans, the team, the coaches deserve better than that.
"From when I was a boy all I wanted to do was play for Scotland, I have given everything I could to that and I don't feel as committed any more.
"It's quite a hard thing to admit to yourself, this has been a massive priority for my whole life and now it isn't.
"But I'm still 100 percent committed to playing for Edinburgh and I just want to knuckle down towards that.
"I'm glad that it's all out there now and I can just get back into training with Edinburgh and focus on turning things round for the club."
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