The Bhoys confirmed that the Scottish midfielders had finally arrived at Celtic Park late on Monday night, and presented Armstrong, as seen above.
Armstrong, 22, burst onto the scene last season with 11 goals and 11 assists, and with a number of great displays at Tannadice this season, it's no surprise to see Celtic snap him up.
Rumours throughout the day suggested the deal was off and then on again, but finally he is a Celtic player after some tough negotiations.
He is joined by Dundee United team mate Mackay-Steven, whose arrival at Celtic was slightly more predictable given that he had already signed a pre-contract agreement with the Bhoys in January.
The 24-year-old was scheduled to join Celtic on a free transfer in the summer, but Celtic have managed to persuade Dundee United into selling him now.
It's an impressive double deal for Celtic, who have made strides to increase the number of Scottish players in their squad - and in Armstrong and Mackay-Steven, they have two of the most promising Scots around.