It's quite a recent phenomenon. The most well-known was the Pont Des Arts in Paris.

Though I found this search result reference which may or may not be true.

"The tradition of attaching padlocks onto the bridge began roughly around 2008. The custom has been traced to a 2006 novel by Frederico Moccia called “I Want You,” which features couples writing their names onto a padlock attached to Rome’s Milvian bridge before throwing the key into the river as a sign of eternal love."