Under the terms of the deal, Adani will pay the amount in two tranches, A$90m ($84m) in cash within five days of the exercise of the option and the balance A$65m ($60.7m) in cash on or before 12 months from the date of the signing the agreement.
The option is expected to be executed within two months.
Linc Energy said that the proposed sale is part of its efforts to offload non-core assets and reduce debt, while strengthening its cash on balance sheet position.
"The Company considers this transaction with Adani to be of benefit to shareholders given current coal market conditions and the projected time to first production from the Carmichael mine," the company said in a statement.
Linc Energy CEO and managing director Peter Bond said: "We look forward to making further announcements as we continue the process of simplifying and focusing our company on the development of our core assets.
"Linc Energy has a number of very good quality assets, the sale of the Adani Royalty for A$155m is a great example of one of these.
The proposed deal comes amid raising questions that whether Adani will proceed with the project as it is being opposed by environmental groups concerned over possible carbon pollution and impacts on ground water supply at the World Heritage-listed the Great Barrier Reef.
Adani purchased the Carmichael mine from Linc Energy for A$500m ($467m) in August 2010 and agreed to pay the royalty stream.
