KPN has been looking for a new CEO since June when Maximo Ibarra quit after just over a year in the job to lead Sky Italia.
On Monday, it dropped its plan to name Belgian executive Dominique Leroy to the job, after she became embroiled in an insider trading investigation in Belgium.
Leroy said she did nothing wrong, but KPN said it could not press ahead with her appointment with the investigation pending.
Farwerck, who is currently the company's chief operating officer and acting CEO, takes the top job with immediate effect as the company seeks to increase underlying earnings after years of declines and stagnation.
He said his aim was "organic, sustainable growth in the Netherlands", on a call with reporters on Tuesday morning.
Asked whether he was bothered by having been "second choice" as CEO, he said he was happy about the opportunity and enthusiastic for the job.
"No, I feel very supported," he added.
"Joost knows the company inside and out," said Chairman Duco Sickinghe, adding that he was confident he could help KPN meet 2019-2021 growth targets.
Separately on Tuesday, KPN announced the wider management shake-up. It said Chief Financial Officer Jan Kees de Jager would leave the company in March 2020 after five years in the job to pursue "international entrepreneurial opportunities".
De Jager, a former politician and Dutch finance minister, will be replaced by the CFO of Dutch insurer ASR, Chris Figee.
Sickinghe said the decisions on Farwerck and an expansion of the company's management board had taken place at a board meeting on Monday night.
The company said it would also add four additional executives to its management board, including a consumer market chief, a business market chief, a chief technology officer and a chief people officer.
(Reporting by Toby Sterling; Editing by Shri Navaratnam, Subhranshu Sahu and Emelia Sithole-Matarise)
By Toby Sterling