Following the international period, players from both clubs will get a chance to head away on holidays after hard-fought seasons.
Both clubs enjoyed successful campaigns, with Celtic taking the league title, while Rangers won the Scottish FA Cup, while also reaching the Europa League final.
It will no doubt be another close title race next term, but before then, we have the summer transfer window, which opens in less than two weeks.
And with that in mind, we have rounded up the latest rumours from both clubs.
Celtic are being linked with a move for Metz midfielder Kevin N'Doram,
Homme de Match in France are reporting Celtic are eyeing the midfielder following Metz’s relegation to Ligue 2.
It’s claimed the Hoops would have to pay around £2.5million to complete the deal this summer, and that price could make Ndoram very tempting.
The Bhoys are also being linked with a move for Bristol City star Antoine Semenyo, amid claims they have been watching the £20million striker.
Journalist Pete O’Rourke told GiveMeSport: “I think he’s someone that Celtic have been watching for quite a long time.
“There was talk of a possible move last summer, and also during the January transfer window, and I’m sure Celtic have continued to monitor his situation. He’s got potential, Semenyo.”
Rangers star Connor Goldson appears to be on his way out of Ibrox, with his contract up at the end of next month.
Goldson wrote on social media: "[A] 60 game season full of highs and lows and ending it with silverware. Days and nights that will stay with me forever."
Could that mean he is on his way out after four years at the club?
According to the Daily Record, the centre-back is already on the verge of selling his house in Glasgow.