Cenk Tosun believes he and Theo Walcott can fill the void created by Romelu Lukaku’s departure from Everton after the winger completed his move from Arsenal for an initial £20m.

Everton have spent more than £40m overhauling their attack this month with an initial £21m paid to bring Tosun from Besiktas followed by the arrival on Wednesday of Walcott. The England international ended a 12-year Arsenal career to become Sam Allardyce’s second signing as Everton manager. He is expected to earn £110,000 a week plus bonuses at Goodison Park – matching his Arsenal salary – over a three-and-a-half year contract.

Allardyce, along with Ronald Koeman and David Unsworth before him, has struggled with the paucity of Everton’s forward options since the club sold Lukaku to Manchester United in the summer and failed to secure a replacement. Tosun, a German-born Turkey international, scored 13 goals for Besiktas this season before moving to Merseyside and he is relishing the opportunity to replace the Belgium international.

“Of course I believe I can do it, otherwise I would not be here,” said the 26-year-old, who could eventually cost Everton £27m. “I think I can do it. Lukaku did really well here but I am hoping to score as many goals as I can and do well.

“I wouldn’t compare myself to Lukaku, I don’t like comparing myself to other players to be honest, but my main aim is to take the team to better places and score as many goals as I can.

“The Premier League is fast football, very strong, high tempo, and I’m a strong player myself. I was born and bred in Germany, I learned my trade there, and I think my character as a player is well suited to this kind of football in England. My biggest dream was to play in the Premier League.”

Tosun made his debut in the 4-0 drubbing at Tottenham Hotspur on Saturday and could make his home debut alongside Walcott in a new‑look attack against West Bromwich Albion this weekend. “Theo Walcott is a great player, a proven player and he did really well for Arsenal for many years,” said the forward, who started his career with Eintracht Frankfurt before moving to Gaziantepspor in Turkey in 2011. He played for Germany under-21s before switching international allegiances to Turkey.

“When you look at Theo he is not an old player but a player with a lot of experience. He will bring a lot to the team. We need that kind of input upfront and I hope he will give that to us. He’s fast, a good crosser and a massive signing for us. I think I’ll link up well with him and the other talented players in the team.”

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Everton beat off competition from Walcott’s former club Southampton to secure the 28-year-old, who scored 108 goals for Arsenal and won three FA Cups. Walcott has not started a Premier League game since April last year, however, having lost a regular role in Arsène Wenger’s side, and he admits Everton’s ambitions offer a chance to revive his career.

Walcott said: “I do really believe I’m going to give it my all, which is what I always have done, and this place is going to get even more out of me. There’s something about this move which I’ve just felt good about. It felt like it was time for me to move on. It was sad but it’s exciting at the same time and I want to reignite my career and push Everton to win things as they have done before.

“The club has won trophies but I want them to win trophies now. The manager is very hungry and it’s just what I need. I’ve had a couple of chats with him and straight away I felt that hunger and that desire that he wanted from me. I need that and I wanted that. I want to be part of something which he’s building. It’s a very ambitious club.”