The 33-year-old was Arsene Wenger's only signing during a quiet transfer window at the Emirates Stadium as the Arsenal boss looked to find a goalkeeper he could fully trust.
Cech, who won 13 major honours during an 11-year stint at Chelsea, moved across London and has played every competitive game since.
He may sit out Wednesday night's third round Capital One Cup clash against fierce local rivals Tottenham, but he has been backed by former Gunners number one Seaman as a man who can turn the club into bona fide championship contenders.
"It is a problem solved for Arsene," Seaman told Press Association Sport.
"You have got a goalkeeper there with great quality, great experience and who commands immediate respect from the Arsenal players for what he has done in the game.
"(David) Ospina has done well and is a little unfortunate to find himself as number two - Wojciech Szczesny has shown inconsistency and you can't do that as Arsenal goalkeeper.
"With Cech you have just got quality
The consistency helps sustain a challenge, it helps the confidence of the defence - they know you're not going to be making mistakes and being rash in games.
"That is what you get with Petr Cech, he won't make many mistakes and he is already showing how good he is despite having a new back four in front of him."
Despite the addition of Cech, many Arsenal supporters were upset that the club did not bolster their outfield options - the only club in the top five European leagues not to do so
But Seaman trusts Wenger and thinks he may dip into the transfer market when the window reopens in the new year, using some of the cash reserve of Â£193.1m revealed last week by financial figures for Arsenal's parent company
"I'm sure in the January window there will be movement, especially now the figures for how much Arsene has to spend have come out," he added
"If they get to January in a strong positon, I'm sure he will strengthen again
"It is brave that he has not listened to everyone and gone and spent money but he is in the same mould as Sir Alex Ferguson - so many people think they know more than Wenger but I'm sorry, they don't
He knows the club better than anyone and knows what they need."
As well as the likelihood being Cech will be rested at White Hart Lane, defender Gabriel and midfielder Santi Cazorla serve suspensions for the red cards they picked up in Saturday's controversial 2-0 defeat at Cech's former side Chelsea.
There is also the prospect that Tottenham head coach Mauricio Pochettino will rotate his squad, meaning Michel Vorm could start ahead of first-choice stopper Hugo Lloris.
France international Lloris was linked with a move away from Spurs in the summer but Seaman is a big fan of Tottenham's new skipper.
"He is really good
He is top, top quality," he said.
"He makes saves that you don't expect him to make
I know he is not a big goalkeeper but he makes the saves, you see the gaps but he gets there.
"He is a top quality goalie
It was all set to move around if David De Gea looked set to leave Man United
I'm sure a goalkeeper of that quality will be wanting to contend for trophies."
:: David Seaman was speaking on behalf of The Football League and Capital One - the credit card in your corner
Source : PA