"Ann Budge (owner), the board of directors and everyone at Heart of Midlothian Football Club would like to sincerely thank Robbie and Stevie for the enormous part they have played in helping to re-establish the club in the upper echelons of Scottish football".
They have now been completed and Neilson becomes the Dons' sixth different permanent manager in their history following Karl Robinson, Roberto Di Matteo, Martin Allen, Danny Wilson and Paul Ince twice. "With the squad that we've got here, we should be winning football matches - our job is to help them do that".
The 36-year-old leaves Hearts second in the Scottish Premiership, replacing Karl Robinson at a side now 19th in England's third tier.
Neilson gave journalists the slip yesterday when a member of his coaching staff, believed to be head of sports science John Hill, donned a face mask of the outgoing head coach, and his coat, as he got into his vehicle and drove off. We wish them every success in their new challenge with Milton Keynes Dons FC.
Neilson is expected to be announced as Dons manager before their Emirates FA Cup tie against Charlton on Saturday.
The Newcastle assistant coach has worked under Steve McClaren and Rafa Benitez at St James' Park following spells as assistant manager at Portuguese top-flight side Rio Ave and Valencia.
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Hearts have made it clear the 30-year-old Scot is the man they want to fill the head coach's role and Cathro is keen to take the opportunity.
In his debut season, Neilson led Hearts to the Scottish Championship title ahead of Rangers and Hibernian with a record points total of 91 while European football was secured in their first season back in the top flight following a third place finish.
Newcastle coach Ian Cathro has been linked with the Tynecastle vacancy. We don't have any official approach.
The impressive young coach has been heavily tipped to take over at Hearts in recent days.
'I'm not going to get involved in talking about individuals, ' he added. "A further statement confirming interim arrangements for our game against Ross County on Saturday, will be released tomorrow morning".