Sunderland decided not to extend Matthews' deal by the end of last season and it took more than three months for the right-back to earn a deal elsewhere, having impressed Charlton on trial.
But despite having received less-than-glowing reviews from some Mackems fans, Bowyer has insisted that Matthews - who is reported to have cost his previous club £2.5 million - will become an important player for his side.
“I can’t believe it [that he was still available],” Bowyer told The South London Press. “He is only 27 and has still got so much more to offer.
“I’m sure working with Jacko [Johnnie Jackson] that he is going to get better, for sure. I couldn’t believe our luck he was on a free.
“He is another good signing. He is a Welsh international and is going to bring us something different. He is definitely going to give us more going forward - his end product is very, very good.
“He has experience at club level and internationally. For me it is a no brainer. He came in and impressed us straight away.
“We have got to get him fit but there are still 40-odd games to go. Adam is definitely going to be important, sooner rather than later.”
Matthews joins his Wales and former Sunderland teammate Jonny Williams at Charlton, after the midfielder re-signed for the Addicks earlier this summer.
The 27-year-old returns to the Championship, where he has played 95 times previously, after a season away.
Sunderland fans - will the Mackems regret not keeping Matthews?
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