The board appointed Thorsten Dirks, chief executive of Telefonica Deutschland, to take over from Karl Ulrich Garnadt who's retiring from the board on 30 April next year. Dirks will take charge of Eurowings from 1 May.
The airline said Dirks' digital expertise will be crucial as it looks to win over customers with new digital services.
Dirks built mobile provider E-Plus and then took over as chief executive officer when it was folded into Telefonica Deutschland AG in 2014.
Carsten Spohr, chief executive of Deutsche Lufthansa AG, said: "Thorsten Dirks has shown that he achieves economic success with firm cost control."
The German airline has ambitions for Eurowings to become Europe's third largest point-to-point carrier and has planned deals to lease up to 40 planes and their crew from rival Air Berlin and take over Brussels Airlines.
But industrial action has been causing headaches for the company. Lufthansa has been battling a raft of strikes by pilots' union Vereinigung Cockpit (VC), which said last week that it required more information from the airline before it would resume failed pay talks. It had carried out six days of strike action, grounding 4,460 flights and causing havoc for 525,000 customers.
In an effort to bring about an end to the strikes, Lufthansa said it was ditching demands for pilots to work more hours in exchange for a rise in wages, and is offering to up pilots' pay by 4.4 per cent in two instalments this year and next.
Eurowings has been battling industrial action of its own and last week reached an agreement over pay with cabin crew staff avoiding further strikes.
It had cancelled more than 60 flights after a strike by cabin crew at Düsseldorf and Hamburg airports.