The two brands were earmarked for closure late last year by Gold Medal parent dnata Travel Group but have been given a reprieve by new entrant, Destinia.
Dnata said its decision to shutter the two brands followed "a detailed review" of its UK travel businesses and a strategic effort to match its brands with "the realities of a changing market".
However, Destinia has stepped in to take them on, stressing both outlets "are established UK brands with a long history and a strong customer base".
"Destinia plans to continue operating the brands while supporting them with its technology and operational platform," it said on Tuesday (20 January), adding the deal would allow it to enter the UK market through brands "already well known to British travellers".
Ricardo Fernandez, chief executive of Destinia Group, said: “Travel Republic and Netflights have built long-term relationships with their customers. Our focus is on keeping the service and booking experience people trust, while supporting the brands with our systems and scale."
Destinia has said it will "prioritise continuity" for customers by building on and expanding the current range of holidays and flights offered by Travel Republic and Netflights where they have "strong directly contracted partnerships".
These include Spain, Portugal, Italy, Greece, Turkey, Egypt, Morocco and Tunisia.