The BPO giant confirmed that Nunn, who was previously managing director of Williams Lea Marketing Solutions and who topped the PrintWeek Power 100 in 2012, left the business in June.
A spokeswoman for the company said: "Steve's role had developed over the past 18 months or so into a broader, more global operations role with print and procurement falling in line as one of the essential service sets provided by the Tag business. As such, there won't be a direct replacement for Steve as Tag COO P&P."
Williams Lea also confirmed that Nunn's fellow chief operating officer at Tag, Tim Cautley, who was responsible for Broadcast and Facilities, also left the business "some months ago to pursue other interests" and will not be replaced.
Ellerton, who took up his post at the beginning of June, has held a number of senior roles at Deutsche Post DHL, which acquired a majority stake in Williams Lea in 2006, including chief development officer at DHL Supply Chain and chief executive officer of DHL's Global Specialist Businesses.
He is based in the UK and has responsibility for Williams Lea, Tag Worldwide and the group's other branded businesses.
Williams Lea said that his appointment "indicates the ongoing commitment to leverage the Deutsche Post DHL client base and solutions to support maintaining market leadership for the Williams Lea businesses".
John Gilbert, CEO Supply Chain and member of the board of management of Deutsche Post DHL, said: "Dan has been pivotal to Deutsche Post DHL's success during the past two decades and, in this new role, we are looking for him to grow our Williams Lea Group businesses and bring those unique propositions and offerings to the marketplace while leveraging the wider group's skills to continue to strengthen its performance and scale its operations."
Ellerton's arrival comes around 20 months after the departure of former CEO Tim Griffiths, who stepped down in October 2012 after 25 years and was initially replaced by Conor Davey, who left the business in May 2013.