Engels joined Celtic from Bundesliga side Augsburg just ahead of the transfer deadline following the earlier arrival of United States centre-back Auston Trusty from Sheffield United on a five-year-deal.
Celtic completed a last-gasp swoop for Dundee midfielder Luke McCowan after earlier breaking their record transfer fee.
Brendan Rodgers got his wish as Celtic signed Arne Engels for a reported £11million as both the champions and Rangers landed late deals on deadline day.
The Scottish champions left it late to sign McCowan, announcing the former Ayr player had signed a three-year deal 45 minutes after the transfer deadline.
The 26-year-old hit 10 goals last season and was Dundee’s player of the year before captaining the side in the absence of the injured Joe Shaughnessy.
Engels joined Celtic from Bundesliga side Augsburg just ahead of the transfer deadline following the earlier arrival of United States centre-back Auston Trusty from Sheffield United on a five-year-deal.
The 20-year-old midfielder was earlier named in the Belgium squad and Rodgers declared his “style of play, his energy and his technical ability really will suit our game model”.
There were two permanent departures from Celtic Park as Mikey Johnston finalised a move to West Brom and Tomoki Iwata joined Birmingham.
Rangers also signed a midfielder and defender as Albania international Nedim Bajrami arrived from Italian side Sassuolo on a permanent deal just before the 11pm deadline.
The Light Blues earlier secured a loan deal for 22-year-old Dutch defender Neraysho Kasanwirjo from Feyenoord with an option to buy next summer.
There have been exits from Ibrox with Scott Wright joining Birmingham for an undisclosed fee and Todd Cantwell moving to Blackburn on a three-year deal.
St Mirren went into Saturday to announce a season-long loan deal for former Motherwell striker Kevin van Veen, whose return to the William Hill Premiership will spell the end of his unhappy spell at Groningen.
The Buddies allowed Ryan Flynn to join Arbroath and sold 18-year-old Ethan Sutherland to Wolves, who also bought young defender Sebastian Lochhead from Dundee.
Hibernian also announced a deal after midnight as they bolstered their defensive options with the signing of 28-year-old former Morton and Queen’s Park centre-back Jack Iredale from Bolton.
Hibs earlier re-signed Nectarios Triantis on a season-long loan deal from Sunderland with David Gray earmarking the Australian for a defensive midfield role.
They allowed Allan Delferriere to join Racing Union Letzebuerg for the duration of the season and loaned Jair Tavares to Motherwell.
The Steelmen also re-signed Jack Vale from Blackburn on a season-long loan.
Dundee United signed 24-year-old Wrexham forward Sam Dalby on a season-long loan. They earlier sold 18-year-old winger Brandon Forbes to Norwich after his recent first-team breakthrough and confirmed that Liam Grimshaw had left Tannadice.
There was a new arrival across the street as well as 19-year-old Austrian midfielder Oluwaseun Adewumi joined Dundee on loan until January immediately after signing for Burnley.
Midfielder Jason Holt returned to St Johnstone on a two-year contract after leaving Livingston at the end of last season while defender Jayden Richardson left Aberdeen.
