Sterilize enough jars and lids to hold relish. Set aside.
Line a large colander with cheesecloth, place in sink or in a large bowl. Set aside.
In a food processor, in batches, coarsely grind tomatoes, red bell peppers, green bell peppers, and then onions.
Pour veggies into cheesecloth-lined colander and allow to drain for an hour.
In a large, non-aluminum stockpot, combine tomato mixture with celery seed, mustard seed, salt, sugar, and vinegar. Bring to a boil and simmer over low heat five minutes, stirring frequently.
Pack relish into sterilized jars, making sure there are no spaces or air pockets. Fill jars all the way to top. Add lids and tightly screw on rings.
Place a rack in the bottom of a large stockpot and fill halfway with boiling water. Carefully lower jars into pot using a holder. Leave a 2 inch space between jars. Pour in more boiling water if necessary, until tops of jars are covered by 2 inches of water. Bring water to a full boil, then cover and process for 30 minutes.
Remove jars from pot and place on cloth-covered or wood surface, several inches apart, until cool. Check to be sure each jar sealed.