The 18-year-old was handed his Premier League debut back in August by Lampard before going to sign a four-year deal with the Blues a fortnight later.
While he has only made one more appearance in the league since then, Gilmour has impressed while with the development squad and was told about his promotion during Chelsea’s visit to Leicester at the start of this month.
‘It’s a massive moment for me and I’m really happy,’ Gilmour told the club’s official website.
‘I went with the squad to Leicester and even though I wasn’t involved, the gaffer pulled me afterwards to tell me that after the winter break I’d be with the first-team permanently.
‘It’s a dream come true for me. It’s the first big step I think, moving into the first team dressing room at a club like Chelsea. It’s massive for me.
‘Knowing that the manager has such faith in you is massive, it gives me so much confidence when I step onto the field.
‘It’s really good knowing that he trusts in you and likes the way you play, and I think that’s the same for everyone here.
‘Age isn’t really an issue here. The gaffer has shown that if you work hard and perform well, then you will get opportunities. Hopefully I can keep pushing on and work hard every day in training.’