The club announced Begg had become joint manager with Kevin Milne last week shortly after their 7-0 demolition of Haddington Athletic in a friendly.
Begg had applied at the same time as Milne but was unable to take up the reins at the time.
Speaking to Penicuik TV, he said: “I’m delighted to be here. My personal circumstances have changed which means I can now come on board at Penicuik.
“Kev and I have known each other and worked together for a long time. We have similar philosophies and ideas on the game so we are dovetailing really great.
“So far things have been great and I’m sure that will continue.”
Cuikie have been impressive this season and sit at the summit of East of Scotland Conference A. They suffered their first defeat in the league after a 2-1 loss to nearest challengers Hill of Beath. Begg believes the emphatic 7-0 win over Haddington was the perfect response from the side.
Wayne McIntosh grabbed a hat-trick while Ryan Baptie scored from the halfway line as Cuikie put their disappointment against the Fifers behind them in some style.
Begg said: “We want to go back on a run after Saturday’s defeat to Hill of Beath.
“Let’s be ruthless and relentless, week after week. We have got a league to try to do our very best to win and then we’ll see where that takes us.
“The Haddington result was a great starting point, the boys were terrific.
“They have done everything we have asked them to do in terms of their possession and movement, be patient and their retention on the ball.
“We had good creativity in the team and created chances. Off the ball our pressing and shape was good.
“We’re really pleased that gets Saturday out of the system and look forward to the rest of the season.”
A statement from the club said: “We are delighted to confirm the appointment of Tony Begg as our co-manager alongside Kevin Milne.
“Tony applied for the job alongside Kevin but due to personal circumstances was unable to take on the role. “However these circumstances have now changed and we are delighted Tony is now able to take on the role as co-Manager alongside Kevin as planned.
“Everyone at Penicuik Athletic wishes both Tony and Kevin all the very best of luck.”
Meanwhile, Cuikie have been busy in the transfer market with goalkeeper Liam Robertson joining the club. Robertson, who has had spells with Tranent, Peebles and Selkirk, came off the bench in the 7-0 friendly win over Haddington.
The club have also signed defender Craig Stevenson from Lowland League champions Spartans. Stevenson spent five seasons with the capital club.