The titles were put up for sale last month after Lloyds Banking Group took control of parent company B.UK Ltd following a long-running dispute over loan repayments.
Lloyds then appointed receivers from AlixPartners at B.UK.
McTighe has vast experience in senior executive roles at tech businesses including Cable & Wireless and Motorola. He was also on the board of Ofcom for eight years, until 2015.
He has been appointed as chair of the board at Telegraph Media Group parent Press Acquisitions, and at May Corporation which is the parent company of The Spectator (1828).
His appointment followed a “thorough, externally-facilitated search process”.
The Times reported there was the prospect of “a bidding war” for the titles, which could go to separate buyers.
Telegraph Media Group had sales of £245m in 2021 and made an operating profit of £30.7m – up from £23.1m the prior year. Print subs brought in £68.6m, up 3%.
The Spectator (1828), had sales of £20.3m in 2021, up from £16.3m in 2020, with operating profits up nearly 85% at £2.9m. The business also publishes Apollo magazine.
The Telegraph and Spectator are trading as normal.