Theodoridis, a 50-year-old Greek citizen, had been Infantino's deputy since October 2010, having joined UEFA in 2008 and initially working in the national associations division.
He will effectively be responsible for running the day-to-day operations of UEFA, a task that includes overseeing this year's European Championship in France which will feature 24 teams in June-July.
UEFA also faces a year that could be critical for the future of the Champions League.
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The format for the competition's 2018-2021 cycle must be decided by the end of the year and there have been suggestions that big clubs are pushing for radical changes, which could include automatic places for some of them.
Theodoridis said UEFA would hold a presidential election as soon as Michel Platini's appeal against his six-year ban had been heard by the Court of Arbitration for Sport (CAS), the highest tribunal in sport.
UEFA has not appointed an acting replacement for Platini and Theodoridis denied there was a power vacuum.
"UEFA has a very strong executive committee and also an administration that throughout the last four months has been run by its competent staff, by its directors and faced no particular issues," he said.
Platini was initially banned and place under investigation in October over a 2 million Swiss franc ($2.02 million) payment he received from FIFA in 2011 for work done for its former president Sepp Blatter nearly a decade earlier.
The Frenchman was banned for eight years along with Blatter in December, and both had their suspensions cut to six years last week by FIFA's Appeal Committee.
"Whenever there is a (CAS) decision, we can hold immediately a meeting of the executive committee meeting and go through an accelerated process for an election," Theodoridis told reporters.
This could happen before Euro 2016, which starts on June 10, if CAS decides in time, he said.
UEFA confirmed that Kosovo's application to become its 55th member would be voted on at its congress in Budapest on May 3. If approved, Kosovo could apply for FIFA for membership in time to play in the 2018 World Cup qualifiers.
UEFA also said that goal-line technology would be used in both the Champions League and Europa League finals in May.
UEFA, which had previously resisted the use of the technology under Platini, had already approved its use at Euro 2016.
($1 = 0.9892 Swiss francs)
(Writing by Brian Homewood; Editing by Ed Osmond)
