The Premier League pair have been hot on the trail of the left-back and United boss Sir Alex Ferguson was said to be particularly keen on the teenager as a potential successor for Patrice Evra.
But Boilesen has rejected the overtures of the English duo by choosing to sign for Dutch giants Ajax.
Sir Alex Ferguson wanted Boilesen to compete with Patrice Evra for the left-back spot
The defender said: 'I am glad that there is clarity about my future. It will be an exciting challenge to play with Ajax.'
Boilesen has signed a three-and-a-half-year contract but Ajax still have to agree a transfer fee with Brondby.
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