Before meeting Harry, Meghan starred in US legal drama series Suits in which she played paralegal-turned-lawyer Rachel Zane.
Bradby said that Harry saw his brother's wife as 'the sister you never had', with the pair having known each other since soon after William and Kate started dating in 2003.
The pair are believed to have got on well, with Harry joining her and William on engagements before he met Meghan - although he told Bradby that while the events were 'fun', he sometimes felt 'slightly awkward' being the 'third wheel'.
Harry also said the idea of himself, his wife and the Prince and Princess of Wales being the 'fab four' was 'something the British Press created' and it 'creates competition'.
He told Bradby: 'The idea of the four of us being together was always a hope for me.
'Before it was Meghan, whoever it was going to be, I always hoped that the four of us would get on.
'But very quickly it became Meghan versus Kate.
'And that, when it plays out so publicly, you can't hide from that, right? Especially when within my family you have the newspapers laid out pretty much in every single palace and house that is around.'
Harry added that his brother William 'raised some concerns' about his marriage to Meghan before their wedding in May 2018.
He said: 'He never tried to dissuade me from marrying Meghan, but he aired some concerns very early, and said 'this is going to be really hard for you' and I still to this day don't truly understand which part of what he was talking about. Maybe he predicted what the British Press's reaction was going to be.'
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