[2] His first goal was an equalizer in injury time against Olympiacos in Karaiskakis Stadium on 7 November 2009, to help Iraklis escape with an away draw against the Greek giants.

[14] Vellios made his first-team debut for Everton against Aston Villa in the Premier League, on 2 April 2011, replacing Jermaine Beckford after 80 minutes.

He made his 2012/13 first team debut by coming on as a sub against Sunderland, which Everton won 2–1 with Marouane Fellaini and Nikica Jelavic getting the goals for the Toffees.

[18] He was given a starting debut at Queens Park Rangers on 29 March, but in the next match — a 2–1 home defeat to Yeovil Town — he was substituted five minutes into the second half and did not feature again.

[22] On 26 September 2015, he equalised for the final score of 1–1 from a Costin Lazăr assist on the fifth day of the Greek Super League against Skoda Xanthi.

[24] On 17 November 2015, Vellios stood alongside Nikos Kyzeridis, giving his jersey for fundraising, thereby demonstrating support for the former Aris player struggling with cancer.

[30] On 7 February 2016, Vellios' 10th Super League goal helped his club to win 1–0 PAS Giannina at Kaftanzogleio Stadium.

Eight days later, having come on as an early substitute for Britt Assombalonga, his penalty was saved in a 4–3 home win against Wigan Athletic in the Championship.

[39] On 1 October, Vellios gave the visitors an early lead at Ashton Gate for his fourth goal of the season in a 2–1 away loss against Bristol City.

[40] In a poll published by the Nottingham Post on 4 October, Forest fans chose Vellios as the best player of the team until that moment, with 39% of the voters picking him.

[44] On 27 January, Vellios came off the bench ten minutes before the end of the game and scored his first goal of the season in a 2–1 loss to Hull City in the FA Cup.

[46] Vellios did not form part of Karanka's plans for 2018–19, and on 31 August 2018, he signed for Waasland-Beveren of the Belgian First Division A on a season-long loan.

[56] On 18 December 2019, he scored a late header from Javier Umbides’ cross five minutes from full-time salvaged the home draw for Atromitos against Lamia.

[62] On 6 July 2022, Vellios signed a one-year contract with recently relegated Dutch Eerste Divisie club PEC Zwolle, with an option for an additional year.

[65] On 3 March 2023, Vellios scored a hat-trick in the 14 first minutes, and four goals total, in a record-tying 13–0 league victory over FC Den Bosch.

[71][72] On 16 March 2016 Vellios was called for the first time to play for the Greece national football team in two friendly matches against Iceland and Montenegro.