Birchall told BBC Radio Kent: "Hessy fired my career up again.
"He took me to Dover and that was the start of a great time in my football career and, hopefully, there are more great things to come," he said.
Birchall started his career at Arsenal and had spells with Mansfield Town and Barnet before joining Dover in 2009 when Hessenthaler was Whites manager.
Birchall scored 45 goals last season, including one in the 2-0 win over the Gills in the FA Cup.
Although Birchall has risen from a non-league side, he is aware there is already pressure on him to perform.
"I know how to deal with the pressure now. If you have high expectations of yourself, it doesn't matter what anyone else says but it's flattering people are saying that. It's not nailed on that it's my place in the side."
Birchall is Gillingham's eighth signing of pre season and is expected to wear a Gills shirt for the first time in Wednesday's friendly with Ramsgate.
He was leading scorer for Barnet when he was there. He knows how to score in this division.
Andy Hessenthaler
Manager Andy Hessenthaler said: "We brought him to Dover when he felt his career wasn't going the right way. The year he was with me, he scored a lot of goals, considering he was out for three months.
"Forty-five goals last season is phenomenal. Swindon and AFC Wimbledon came in but the kid wants to progress and nobody can deprive him of that.
"Birch has played in this division and was the leading scorer for Barnet when he was there. He knows how to score in this division."
The club's other new striker Danny Kedwell scored his first goal in a Gillingham shirt in Tuesday's friendly with Erith and Belvedere. Gillingham won 5-0 with Luke Rooney scoring twice and both Gary Richards and trialist Paris Cowan-Hall also on target.
Source: BBC Sport
Source: BBC Sport