A statement on the RAF website said the move allowed it to "ensure the fighter jets are always ready to respond at a moment’s notice".
The exercise saw the squadron given a short notice order to "relocate and be prepared to rapidly commence operations" from RAF Leeming.
It said the Typhoons have been relocated to the North Yorkshire base on a temporary basis.
Group Captain Prendergast, Station Commander at RAF Leeming, said: "The Royal Air Force stands ready to defend UK airspace at a moment’s notice – it’s what we do.
"Working closely with our Lossiemouth counterparts, I was incredibly impressed by the professionalism and efficiency with which our personnel ensured that RAF Leeming was ready to accommodate this vital capability rapidly and successfully."
Wing Commander McAuley, Officer Commanding Operations Wing, added: "RAF Lossiemouth personnel from a range of professions, in partnership with RAF Leeming, have worked tirelessly to ensure the QRA capability continues to maintain the security of the UK Airspace.
"This temporary relocation of Quick Reaction Alert to RAF Leeming showcases the RAF’s agility in delivering our capabilities. Being able to respond quickly and professionally in an exercise or operational scenario is at the centre of what we do as a force."