Coming off the bench against the Ospreys, Jacobsen helped Edinburgh to a first league win since mid-September and Bradley revealed that the prop is a player reborn since taking the decision to call time on his Scotland career.
He said: "Allan Jacobsen is running around like a 21-year-old with us at the moment. I think that the pressure is off his shoulders and he's enjoying it.
"The demands of international rugby are very high and he felt it was time to walk away. He is still very committed to Edinburgh and is playing an important part in this squad.
"He's been an important member of the Edinburgh squad for a long time and we are looking forward to him carrying on in that vein."
A rejuvenated Jacobsen is not the only addition to Edinburgh's squad as they look to get their season back on track, who had lost five straight matches before defeating the Ospreys.
Among the internationals on their way back to Murrayfield is centre Matt Scott, who will be a welcome return following his displays in a Scotland jersey.
And while Bradley admits Scott is still a rough diamond, he was impressed by his efforts for Scotland.
He added: "Matt has become a key member of the squad here and although he's got his chance pretty early he looks to have taken it for Scotland.
"It will be a boost to have the guys back because it's fair to say the results haven't been as we would have liked so far this season.
"There is a determination to put things right though. We know that one or two decisions have been costly at times for us and that is something we need to improve.
"We know there is a lot of quality in the squad but we recognise we haven't taken some of the chances we should have done.
"There have been a few narrow losses which could have gone either way but we have to work on the things that we can control and the results will come."
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