Prime Minister Modi also thanked Prime Minister Abbott for hosting a dinner at the Melbourne Cricket Ground (MCG) on the last day of his stay in Australia.
"With my friend @TonyAbbottMHR at the MCG," the Prime Minister wrote, with both leaders also autographing the frame.
"Thank you @TonyAbbottMHR for the wonderful dinner at @MCG. Enjoyed being at this iconic ground," he added.
The Prime Minister also extended his thanks to Australia for making his stay in that country memorable.
"Thank you Australia! Past few days have been excellent. Sharing some photos from this memorable visit," he tweeted.
Earlier in the day, Prime Minister Modi visited a war memorial and addressed the Australian Parliament in Canberra before departing for Melbourne, where he attended a meeting with business leaders and visited the MCG.
After concluding his visit of Australia , Prime Minister Modi will travel to Fiji as the third leg of his three-nation, 10-day trip.