Gregory's ServerThe word 'welcome' may be interpreted as 'well-come', like 'well-received' and 'well-deserved'.
However, it stems from a Germanic word meaning "desired guest".
Perhaps under the influence of French 'bienvenu' ("welcome", literally "well-come"), the perception and the form of the English word and its Germanic cognates were altered. The infographic shows how.
1/
2/
Due to lack of space, unfortunately I wasn't able to include the North-Germanic forms, such as Icelandic 'velkominn', Danish and Norwegian Bokmål 'velkommen', Nynorsk 'velkomen', and Swedish 'välkommen'. These may be loan translations of Middle Low German/Saxon 'wil(le)komen'.
Middle English had multiple other compound words containing 'wil-', such as 'wilspell' ('desired news'), 'wildaȝe' ('desired day'), 'wiltidende' ('desired tiding'), and 'wilgomen' ('pleasant sport').