The new Hawk-Eye system will instantly send a message to the referee that the ball has crossed the line via a special watch.
However, Wenger insists football must also start using technology for other key decisions - such as offside - to help eradicate any perceived injustice, like those in this week's Champions League semi-finals where Borussia Dortmund netted controversial late goals to defeat Malaga.
"It's good news and I hope there is more good news to come on technology because we want the right decisions to be taken. The more assistance the referees get, the better it is," said Wenger.
"When you look at the level of refereeing that you have seen again in Europe this week, it is absolutely disastrous what happened. The major decisions that have gone wrong in the Champions League, football cannot accept that lasts.
"When you have four players that are offside and nobody sees it, how can that happen? In the same action, another player is offside and scores a goal, and we stand here and defend that? It is not defendable.
"I don't believe technology would slow the game down at all if it is done in the right way.
"I am amazed we are just resistant by principle in our sport to move forward for more justice. If it is to get more decisions right then we all have to fight for it."
Meanwhile, Manchester United manager Sir Alex Ferguson has also welcomed the introduction of goal-line technology.
"Progress is progress. It had to happen," he said. "It should be applauded. When you are continually trying to progress your football, it is for the betterment of the game.
"Other sports have been doing it for a long time - and I think it was time football did catch up."