Johnson, who was struck down by viral encephalitis in April 2010, will instead spend time with his family before becoming Scotland's senior assistant coach in May.
"The next few months will allow me to head back to Australia to catch up with my family and to get over the illness that I've suffered with over the last two years," said Johnson.
"I'll take up the post with Scotland at the end of the season. I'll leave with only happy memories from my time with the Ospreys and I've made some great mates for life among the business.
"When I informed the board in December that I wouldn't be renewing my contract, I made the offer to stand down at that time, but they felt that it would be better for the organisation if I remained in office to help provide some stability during what was inevitably going to be something of a transitional period.
"Since then, we've been in constant dialogue and, six weeks down the line, we've agreed that the time is right for me to move on, so we've shaken hands and I'm walking away early from the remainder of my contract."